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YS
2
IM
9 tháng 10 2016
\(\left(x+1\right)^{200}=\left(2x-3\right)^{200}\)
\(\Rightarrow2x-x=1+3\)
\(\Rightarrow x=4\)
Vậy x = 4
9 tháng 10 2016
\(\left(x+1\right)^{200}=\left(2x-3\right)^{200}\)
\(\Rightarrow x+1=2x-3\)
\(\Rightarrow x-2x=-3-1\)
\(\Rightarrow-x=-4\)
\(\Rightarrow x=4\)
Vậy \(x=4\)
9 tháng 10 2016
Vì: \(\left(x-12+y\right)^{200}\ge0;\left(x-4-y\right)^{200}\ge0\)
=> \(\left(x-12+y\right)^{200}+\left(x-4-y\right)^{200}\le0\)
\(\Leftrightarrow\left(x-12+y\right)^{200}+\left(x-4-y\right)^{200}=0\)
\(\Leftrightarrow\begin{cases}x-12+y=0\\x-4-y=0\end{cases}\)\(\Leftrightarrow\begin{cases}x+y=12\\x-y=4\end{cases}\)\(\Leftrightarrow\begin{cases}x=8\\y=4\end{cases}\)
18 tháng 9 2016
1) \(\left(9^9\right)^{2013}\)= 10269363159364666440076552322773341581561034085240554413684171629845226550910869063141084455165024846467308031862801839537350602585807388907790165677831287422774432660306450530003706882130019126660033621304145739244276173577048090504994820917529469442173652905242934472777858750567472632994664600381934224746675284242716804187707473971153049296389564538282393321100521850729158342672916978486633073346395087524709304026115423816203365757494638423131935882476286148041225377521573071731453557120367321995775004742604569764745022389412766013722532450077367619939069300519001702898185102392773927389960480888542356324726363237536898205586978830302184325193226223435916070961038034935786871565694168032483034776261863802471075705726878653433383001001189241926035182758070542398573188268383074169109020402590360496218759242201271963792394715618265594345634230758007244699004003000401590521959773595723533039737036430015710879179131370760647094133072554170794993632842471406497462695365166916803272574522454401382663974485565680530010978750425197889269057395033275863668478654934441334494555064318484689342316306971521024595876939555467943409513599739742465719710957307401039466505018857934554613930415045936664298639272058657312601916520149572941057253546060280658091085857108287350235860520376248626158812551702239866122771402598673086936929135243309297996461647086887656015121093133495745098227813854645587494331845951709269358587499740880686161437051001446721645931603701931366046756571915591346082194099535179864942435147889719664866893951993209328180552969033445416386172074158156509068184846110009877655498411796133585929465285105476632644661698885141470189436283199349798153583068536942505793691702852246620602269418445330834508954131444268765759312479343419904740139320879242064290138393396190814854006875023217633358501559386869629903562803482598907058580834642187008732774069291138122707731009317247214463199502007349382592744206845610622073119291353793177956259701743316926165329688122906721927196323010889181055169806499566546884164914042278508330036064549558133226697031247070510887763306579421433675607558954912396327853467424003335216349883637063258300867587330031070320552690888583962060709425761455244473416175295550790206629899652326841562128125494362697380378913996157037213809010909152617053065047965873644302701915161491422477028822914991812751244014648364815652852259663562101505343929698300364745277267393347355428142967482152321747112276920645950373078036691708170463157769001081433039723940115958277368318945023698370418990114114623681030598771547893253242183396733689941466450154464716467140441700170890131070394317235669249736167939422225531914712053400394591025170046527933941931808727717700810490226657457458014925192262802223793377911267650955266657089009585212112836905894381397018270698103556284576894624491741924724548232777077039317695115234021720883233465113399660643038825392305224594945823567653088326327442095353311628349624602121813895038502370886964075117719039885809760171422727129924473839457315768243597403319870636550055160900303769922718752206531201831705424385675834623470898120798414884603237556758496483422249797988913495971144948857810070808962140027449957839158509072309335228612816014153586809180977765327121627937134049967684345369108329599698221680897904237253646696104638289317058937956786704502654705018578331925049052381574371364079244827076900746007044670044607514934428774185406569688113571812978834960339563464520445275203854387799426090303262175550913985879685323013395273140584906121284898600419987993686188204435391094252218471390818917130390872182868519308994839897218982949442429019573247952912905380490755419913598457819276169417786284482347581370093174347981877489100149059409603635202204843390807300768332120719828797936653584404544694348383212549192087418173867785361221768506688864308755986946608953282003111974359205430482715512293489410742551889057944409965962731729135907369164794520884407474498460942159861999051690799986820439014933471232036918567390365835132305185662258913590669721711271035876498544692676850173083777815138713451735852959497582505542139720996338872994246201493700854225531805769779199297405335600737006903257207290820931044945024227595231128387120276064384227546402934361068266072587525725727012002788329077620146531366428926553058456985976818503072684025934586637898483958234508662818031180715524520776171094013494021013676728110150423914944710134238003487063081238423668330925015539056597900840885380931769197169725833541445689013104266424340197869967258623982371657927554051872347209361532830788078019771804179098819400418948649540270834597079029891053990824778600110747558315677420029212621805618132160031130257415664172691492945292697559304231368145501988941653172710920650443181254274948908249495935867675652007874393961066550920282780133604505587836446569409476792952876000047659924818891904298270222076421357886611744774356481805662861913303332953231470607411006298630956870297224099368538952834326914631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JE
13 tháng 6 2018
1)
a) Theo đề ta có:
(99)2013 = 99.2013= 918117
Ta có:
91 = 9 có chữ số tận cùng là 9
92 = 81 có chữ số tận cùng là 1
và 918117 = 92.9058. 9 = (92)9058 .9 ( mình giải thích thêm là mình nhân 9 để cùng cơ số và cộng các tử lại là 2.9058 + 1 = 18117)
Vì 92 có chữ số tận cùng là 1
Nên (92)9058 cũng có chữ số tận cùng là 1
\(\Rightarrow\)918117 = (...1) .9
\(\Rightarrow\)918117 = (...9)
Vậy chữ số tận cùng của (99)2013 là 9
b) Ta có:
20081 = 2008 có chữ số tận cùng là 8
20082 = (...4) có chữ số tận cùng là 4 (vì 8.8=64)
20083 = (...2) có chữ số tận cùng là 2 (vì 4.8=32)
20084 = (...6) có chữ số tận cùng là 6 (vì 2.8=16)
và 2008100 = 20084.25= (20084)25
Vì 20084 có chữ số tận cùng là 6
Nên (20084)25 cũng có chữ số tận cùng là 6
Vậy 2008100 có chữ số tận cùng là 6
24 tháng 7 2017
\(\left(x-3\right)^2+\left(y+2\right)^2=0\)
\(\left\{{}\begin{matrix}\left(x-3\right)^2\ge0\forall x\\\left(y+2\right)^2\ge0\forall y\end{matrix}\right.\)
\(\Rightarrow\left(x-3\right)^2+\left(y+2\right)^2\ge0\)
Dấu "=" xảy ra khi:
\(\left\{{}\begin{matrix}\left(x-3\right)^2=0\Rightarrow x-3=0\Rightarrow x=3\\\left(y+2\right)^2=0\Rightarrow y+2=0\Rightarrow y=-2\end{matrix}\right.\)
đề sai câu b các câu sau áp dụng tương tự
24 tháng 7 2017
c/ Vì: \(\left(x-12+y\right)^{200}+\left(x-4-x\right)^{200}=0\)
mà \(\left\{{}\begin{matrix}\left(x-12+y\right)^{200}\ge0\forall x,y\\\left(x-4-y\right)^{200}\ge0\forall x,y\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\left(x-12+y\right)^{200}=0\\\left(x-4-y\right)^{200}=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x-12+y=0\\x-4-y=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x+y=12\\x-y=4\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=8\\y=4\end{matrix}\right.\)
NH
24 tháng 7 2017
mình làm lại câu b) nha
b) |x-3|=-4
th1: x-3=-4
x=3+(-4)
x=-1
th2: x-3=4
x=3+4
x=7
NH
24 tháng 7 2017
b) \(\left|x-3\right|=-4\)
t/h1:\(x-3=-4\)
\(x=3-\left(-4\right)\)
\(x=7\)
t/h2:\(x-3=4\)
\(x=3-4\)
\(x=-1\)
25 tháng 7 2020
\(\frac{1}{3}.3^n+5.3^{n-1}=162\)
<=> \(3^{n-1}+5.3^{n-1}=162\)
<=> \(3^{n-1}\left(1+5\right)=162\)
<=> \(3^{n-1}.6=162\)
<=> \(3^{n-1}=162:6\)
<=> \(3^{n-1}=27\)
<=> \(3^{n-1}=3^3\)
<=> n - 1 = 3
<=> n = 3 + 1 = 4
Y
25 tháng 7 2020
Câu 1
a) Từ gt=>\(\hept{\begin{cases}x-5=1-3x\\x-5=3x-1\end{cases}}\)
<=>\(\hept{\begin{cases}4x=6\\2x=-4\end{cases}}\)
<=>\(\hept{\begin{cases}x=\frac{3}{2}\\x=-2\end{cases}}\)
b) Ta có: \(\hept{\begin{cases}\left(3x-1\right)^{100}\ge0,\forall x\in R\\\left(2y+1\right)^{200}\ge0,\forall x\in R\end{cases}}\)
Kết hợp với đề bài => \(\hept{\begin{cases}3x-1=0\\2y+1=0\end{cases}}\)
=>\(\hept{\begin{cases}x=\frac{1}{3}\\y=-\frac{1}{2}\end{cases}}\)
Bài 2
\(\frac{1}{3}.3^n+5.3^{n-1}=162\)
<=>\(3^{n-1}+5.3^{n-1}=162\)
<=>\(6.3^{n-1}=162\)
<=>\(3^{n-1}=27=3^3\)
<=>\(n-1=3\)
<=>\(n=4\)
5 tháng 8 2017
2) \(\dfrac{x}{y}=\left(\dfrac{x}{y}\right)^2\)
\(\Rightarrow\left(\dfrac{x}{y}\right)^2-\dfrac{x}{y}=0\)
\(\Rightarrow\dfrac{x}{y}\left(\dfrac{x}{y}-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}\dfrac{x}{y}=0\Rightarrow x=0;y\in R\\\dfrac{x}{y}-1=0\Rightarrow\dfrac{x}{y}=1\Rightarrow x=y\end{matrix}\right.\)
3) \(16^5+2^{15}=\left(2^4\right)^5+2^{15}=2^{20}+2^{15}=2^{15}.2^5+2^{15}.1=2^{15}.33⋮33\rightarrowđpcm\)
4)\(\left(x-3\right)^2+\left(y+2\right)^2=0\)
\(\left\{{}\begin{matrix}\left(x-3\right)^2\ge0\\\left(y+2\right)^2\ge0\end{matrix}\right.\)
\(\Rightarrow\left(x-3\right)^2+\left(y+2\right)^2\ge0\)
Dấu "=" xảy ra khi:
\(\left\{{}\begin{matrix}\left(x-3\right)^2=0\Rightarrow x-3=0\Rightarrow x=3\\\left(y+2\right)^2=0\Rightarrow y+2=0\Rightarrow y=-2\end{matrix}\right.\)
\(\left(x-12+y\right)^{200}+\left(x-4-y\right)^{200}=0\)
\(\left\{{}\begin{matrix}\left(x-12+y\right)^{200}\ge0\\\left(x-4-y\right)^{200}\ge0\end{matrix}\right.\)
\(\Rightarrow\left(x-12+y\right)^{200}+\left(x-y-4\right)^{200}\ge0\)
Dấu "=" xảy ra khi:
\(\left\{{}\begin{matrix}\left(x-12+y\right)^{200}=0\\\left(x-y-4\right)^{200}=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x-12+y=0\Rightarrow x+y=12\\x-y-4=0\Rightarrow x-y=4\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\left(x+y\right)+\left(x-y\right)=12+4\Rightarrow x+y+x-y=16\Rightarrow2x=16\Rightarrow x=8\\y=8-4=4\end{matrix}\right.\)
KT
6 tháng 4 2018
a) \(f\left(x\right)-g\left(x\right)+h\left(x\right)\)
\(=x^3-2x^2+3x+1-\left(x^3+x-1\right)+\left(2x^2-1\right)\)
\(=x^3-2x^2+3x+1-x^3-x+1+2x^2-1\)
\(=2x+1\)
b) \(f\left(x\right)-g\left(x\right)+h\left(x\right)=0\)
\(\Leftrightarrow\)\(2x+1=0\)
\(\Leftrightarrow\)\(x=-\frac{1}{2}\)
T
21 tháng 7 2019
#)Giải :
a) \(\left(5x+1\right)^2=\frac{36}{49}\Leftrightarrow\left(5x+1\right)^2=\left(\frac{6}{7}\right)^2\Leftrightarrow5x+1=\frac{6}{7}\Leftrightarrow5x=-\frac{1}{7}\Leftrightarrow x=-\frac{1}{35}\)
b) \(\left(x-\frac{2}{9}\right)^3=\left(\frac{2}{3}\right)^6\Leftrightarrow\left(x-\frac{2}{9}\right)^3=\left[\left(\frac{2}{3}\right)^2\right]^3\Leftrightarrow x-\frac{2}{9}=\left(\frac{2}{3}\right)^2=\frac{4}{9}\Leftrightarrow x=\frac{2}{3}\)
c) \(\left(8x-1\right)^{2x+1}=5^{2x+1}\Leftrightarrow8x-1=5\Leftrightarrow8x=6\Leftrightarrow x=\frac{6}{8}\)
C
21 tháng 7 2019
a) \(\left(5x+1\right)^2=\frac{36}{49}\)
\(\left(5x+1\right)^2=\frac{6^2}{7^2}\)
\(\left(5x+1\right)^2=\left(\frac{6}{7}\right)^2\)
\(\Leftrightarrow5x+1=\frac{6}{7}\)
\(5x=\frac{6}{7}-1\)
\(5x=\frac{6}{7}-\frac{7}{7}\)
\(5x=-\frac{1}{7}\)
\(x=-\frac{1}{7}\div5\)
\(x=-\frac{1}{7}\times\frac{1}{5}\)
\(x=-\frac{1}{35}\)
Vậy \(x=-\frac{1}{35}\)
(x+1)200= (2x-3)200
=> x+1=2x-3
=> x-2x= 1-3
=> -x= -2
=> x=2
(x + 1)200 = (2x - 3 )200
x + 1 = 2x - 3
x + 1 - 2x = -3
-x + 1 = -3
-x = -3 - 1
-x = -4
x = 4
Vậy x = 4