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a. Xét phân số trung gian là \(\dfrac{72}{78}\) , ta thấy:
\(\dfrac{72}{73}>\dfrac{72}{78}\)
\(\dfrac{58}{78}< \dfrac{72}{78}\)
\(\Rightarrow\dfrac{72}{73}>\dfrac{58}{78}\)
b. Xét phân số trung gian là \(\dfrac{n}{n+2}\) , ta thấy:
\(\dfrac{n}{n+3}< \dfrac{n}{n+2}\)
\(\dfrac{n}{n+2}< \dfrac{n+1}{n+2}\)
\(\Rightarrow\dfrac{n}{n+3}< \dfrac{n+1}{n+2}\)
c. Ta có: \(\dfrac{10^{11}-1}{10^{12}-1}< 1\) (vì tử < mẫu)
\(\Rightarrow\dfrac{10^{11}-1}{10^{12}-1}< \dfrac{\left(10^{11}-1\right)+11}{\left(10^{12}-1\right)+11}=\dfrac{10^{11}+10}{10^{12}+10}=\dfrac{10^{10}+1}{10^{11}+1}\)
Vậy \(\dfrac{10^{11}-1}{10^{12}-1}< \dfrac{10^{10}+1}{10^{11}+1}\)
d. Xét phân số trung gian là \(\dfrac{1}{4}\) , ta thấy:
\(\dfrac{12}{47}>\dfrac{12}{48}=\dfrac{1}{4}\)
\(\dfrac{19}{77}< \dfrac{19}{76}=\dfrac{1}{4}\)
\(\Rightarrow\dfrac{12}{47}>\dfrac{19}{77}\)
a. 2333 = (23)111= 8111
3222= (32)111= 9111
Thấy 8<9 nên 8111< 9111.
Vậy 2333 < 3222
b.\(\sqrt{8}\)+\(\sqrt{24}\)
8= 3+5= \(\sqrt{9}\)+\(\sqrt{25}\)
Thấy 9>8; 25>24 nên \(\sqrt{9}\)>\(\sqrt{8}\); \(\sqrt{25}\)>\(\sqrt{24}\)
Vậy \(\sqrt{8}\)+\(\sqrt{24}\)<8
c.Vì 4>3 và \(\sqrt{19}\)> \(\sqrt{15}\)nên 4+\(\sqrt{19}\)>\(\sqrt{15}\)+3
Vậy 4+\(\sqrt{19}\)> \(\sqrt{15}\)+3
a) Ta thấy:
\(\frac{x}{2}=\frac{y}{3}\)\(\Rightarrow\frac{x}{2}\cdot\frac{3}{5}=\frac{y}{3}\cdot\frac{3}{5}\)\(\Rightarrow\frac{3x}{10}=\frac{y}{5}\)
Mà \(\frac{y}{5}=\frac{z}{6}\) nên ta có biểu thức: \(\frac{3x}{10}=\frac{y}{5}=\frac{z}{6}\) ( 1 )
Biểu thức ( 1 ) tương đương với:
\(\frac{3x}{10}=\frac{3y}{15}=\frac{3z}{18}=\frac{3x+3y+3z}{10+15+18}=\frac{3\left(x+y+z\right)}{43}=\frac{3\cdot43}{43}=3\)
Khi đó:
\(\frac{3x}{10}=3\) \(\Rightarrow x=\frac{3\cdot10}{3}=10\)
\(\frac{3y}{15}=3\)\(\Rightarrow\frac{y}{5}=3\) \(\Rightarrow y=3\cdot5=15\)
\(\frac{3z}{18}=3\)\(\Rightarrow\frac{z}{6}=3\) \(\Rightarrow z=3\cdot6=18\)
a, Nhân cả hai vế cho 5, ta được: X/10 = Y/15
Tương tự ta có: Y/15 = Z/18
Do đó: X/10 = Z/18 (=Y/15)
Theo đề bài, ta có: (X+Y+Z)/(10+15+18) = 43/43 = 1
X/10=1 => X=10
Y/15=1 => Y=15
Z/18=1 => Z=18
\(A=17\dfrac{2}{31}-\left(\dfrac{15}{17}+6\dfrac{2}{31}\right)=17\dfrac{2}{31}-\dfrac{15}{17}-6\dfrac{2}{31}\)
\(=11-\dfrac{15}{17}=\dfrac{172}{17}\)
\(B=\left(31\dfrac{6}{13}+5\dfrac{9}{41}\right)-36\dfrac{6}{12}=36\dfrac{363}{533}-36\dfrac{6}{12}=\dfrac{193}{1066}\)
\(C=27\dfrac{51}{59}-\left(7\dfrac{51}{59}-\dfrac{1}{3}\right)=27\dfrac{51}{59}-7\dfrac{51}{59}+\dfrac{1}{3}=20+\dfrac{1}{3}=\dfrac{61}{3}\)
\(A=17\dfrac{2}{31}-\left(\dfrac{15}{17}+6\dfrac{2}{31}\right)=17\dfrac{2}{31}-\dfrac{15}{17}-6\dfrac{2}{31}\)
\(=\left(17\dfrac{2}{31}-6\dfrac{2}{31}\right)-\dfrac{15}{17}=11-\dfrac{15}{17}=\dfrac{172}{17}\)
\(B=\left(31\dfrac{6}{13}+5\dfrac{9}{41}\right)-36\dfrac{6}{12}=36\dfrac{363}{533}-36\dfrac{1}{2}=\dfrac{193}{1066}\) (Casio :>)
\(C=27\dfrac{51}{59}-\left(7\dfrac{51}{59}-\dfrac{1}{3}\right)=27\dfrac{51}{59}-7\dfrac{51}{59}+\dfrac{1}{3}\)
\(=20+\dfrac{1}{3}=\dfrac{61}{3}\)
\(a,8^7-2^{18}=2^{21}-2^{18}=2^{17}\left(2^4-2\right)=14.2^7⋮14\)
\(b,10^6-5^7=2^6.5^6-5^7=5^6\left(2^6-5\right)=59.5^6⋮59\)
c ko nói chia hết cho số nào
\(d,3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}\)
\(=3^{n+1}\left(3^2+3\right)+2^{n+1}\left(2^2+2\right)\)
\(=3^{n+1}.12+2^{n+1}.6\)
\(=6.\left(3^{n+1}.2+2^{n+1}\right)⋮6\)
\(a)3\dfrac{1}{2}.\dfrac{4}{49}-\left[2,\left(4\right):2\dfrac{5}{11}\right]:\left(\dfrac{-42}{5}\right)\)
\(=\dfrac{7}{2}.\dfrac{4}{49}-\dfrac{88}{27}:\left(\dfrac{-42}{7}\right)\)
\(=\dfrac{2}{7}-\dfrac{-220}{567}\)
\(=\dfrac{382}{567}\)
các phần con lại dễ nên bn tự lm đi nhé mk bn lắm
Chúc bạn học tốt!
a) \(x^2-\frac{2}{5}x< 0\)
\(\Leftrightarrow x\left(x-\frac{2}{5}\right)< 0\)
\(\Leftrightarrow\begin{cases}x>0\\x< \frac{2}{5}\end{cases}\) hoặc \(\begin{cases}x< 0\\x>\frac{2}{5}\end{cases}\) (loại)
\(\Leftrightarrow0< x< \frac{2}{5}\)
b) \(\frac{x-2}{x-6}< 0\)
\(\Leftrightarrow\begin{cases}x>2\\x< 6\end{cases}\) hoặc \(\begin{cases}x< 2\\x>6\end{cases}\) (loại)
\(\Leftrightarrow2< x< 6\)
c) \(\frac{x^2-1}{22}< 0\)
\(\Leftrightarrow\left(x-1\right)\left(x+1\right)< 0\)
\(\Leftrightarrow\begin{cases}x>1\\x< -1\end{cases}\) (loại) hoặc \(\begin{cases}x< 1\\x>-1\end{cases}\)
\(\Leftrightarrow-1< x< 1\)
a, -(-12) + (+19) - (+12) + 8 - 19
= 12 + 19 - 12 + 8 - 19
= ( 12 - 12) + ( 19- 19) + 8
= 0 + 0 + 8
= 8
b, (59 - 78) - (42 - 78 + 59)
= 59 - 78 - 42 + 78 - 59
= (59 - 59) - 42 - ( 78 - 78)
= 0 - 42 - 0
= -42
c, ( - 68 + 103) - (-50 - 68 + 103)
= -68 + 103 + 50 + 68 - 103
= (-68 + 68) + ( 103 - 103) + 50
= 0 + 0 + 50
= 50
a) \(...=12+19-12+8-19=8\)
b) \(...=-19-23=-42\)
c) \(...=35-\left(-15\right)=35+15=50\)