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TY
30 tháng 10 2018
a) Ta có: 3x = 2y; 4x = 2z
⇒ \(\dfrac{x}{2}=\dfrac{y}{3};\dfrac{x}{2}=\dfrac{z}{4}\)
⇒ \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}\) và x + y + z = 27
Áp dụng tính chất dãy tỉ số bằng nhau, ta có:
\(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}=\dfrac{x+y+z}{2+3+4}=\dfrac{27}{9}=3\)
⇒ \(\dfrac{x}{2}=3\) ⇒ x = 6
\(\dfrac{y}{3}=3\) ⇒ y = 9
\(\dfrac{z}{4}=3\) ⇒ z = 12
Vậy x = 6 ; y = 9 ; z = 12
b) Ta có: \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}\)
⇒ \(\dfrac{x^2}{4}=\dfrac{y^2}{9}=\dfrac{z^2}{16}\)
⇒ \(\dfrac{2x^2}{8}=\dfrac{3y^2}{27}=\dfrac{5z^2}{80}\)
và 2x2 + 3y2 - 5z2 = -405
Áp dụng tính chất dãy tỉ số bằng nhau, ta có:
\(\dfrac{2x^2}{8}=\dfrac{3y^2}{27}=\dfrac{5z^2}{80}\)=\(\dfrac{2x^2+3y^2-5z^2}{8+27-80}=\dfrac{-405}{-45}=9\)
+) \(\dfrac{2x^2}{8}=9\) ⇒ 2x2 = 72 ⇒ x2 = 72 : 2
⇒ x2 = 36 ⇒ x = 6 hoặc x = -6
+) \(\dfrac{3y^2}{27}=9\) ⇒ 3y2 = 243 ⇒ y2 = 243 : 3
⇒ y2 = 81 ⇒ y = 9 hoặc y = -9
+) \(\dfrac{5z^2}{80}=9\) ⇒ 5z2 = 720 ⇒ z2 = 720 : 5
⇒ z2 = 144 ⇒ z = 12 hoặc z = -12
Vậy...................................( bạn tự vậy nhé )
c) Giống câu a ( bạn tự chép lại )
d) Mik ko bt lm
30 tháng 10 2018
CÂU TRẢ LỜI RẤT HAY BẠN NÀO ĐANG CẦN THÌ THAM KHẢO NHÉ!!!!!!!!
DT
2
N
30 tháng 10 2019
b) \(\left(3x-1\right)^3=-\frac{8}{27}\)
\(\left(3x-1\right)^3=\left(-\frac{2}{3}\right)^3\)
\(\Rightarrow3x-1=-\frac{2}{3}\)
\(3x=-\frac{2}{3}+1\)
\(3x=\frac{1}{3}\)
\(x=\frac{1}{3}:3\)
\(x=\frac{1}{3}.\frac{1}{3}\)
\(x=\frac{1}{9}\)
Vậy x = 1/9
c) |2x + 1| - 3 = 6
|2x + 1| = 6 + 3
|2x + 1| = 9
=> |2x + 1| ∈ {9;-9}
\(\Rightarrow\hept{\begin{cases}2x+1=9\\2x+1=-9\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}2x=9-1\\2x=-9-1\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}2x=8\\2x=-10\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x=8:2=4\\x=-10:2=-5\end{cases}}\)
Vậy x ∈ {4;-5}
HN
5 tháng 7 2017
1) Tính
a) 253 : 52 = (52)3 : 52 = 56 : 52 = 54 = 625
\(b)\left(\dfrac{3}{7}\right)^{21}:\left(\dfrac{9}{49}\right)^6=\left(\dfrac{3}{7}\right)^{21}:\left[\left(\dfrac{3}{7}\right)^2\right]^6=\left(\dfrac{3}{7}\right)^{21}:\left(\dfrac{3}{7}\right)^{12}=\left(\dfrac{3}{7}\right)^9\) d) 9 . 32 . \(\dfrac{1}{81}\) . 32 = 32 . 32 . \(\dfrac{1}{3^4}\) . 32 = 9
2) Tìm x thuộc Q, biết:
a) 3x + 2 = 27
=> 3x + 2 = 33
x + 2 = 3
x = 3 - 2
x = 1
b) \(\left(\dfrac{1}{2}x-3\right)^4=81\)
\(\Rightarrow\left(\dfrac{1}{2}x-3\right)^4=3^4\)
\(\dfrac{1}{2}x-3=3^{ }\)
\(\dfrac{1}{2}x=3+3\)
\(\dfrac{1}{2}x=9\)
\(x=9:\dfrac{1}{2}\)
\(x=18\)
c) \(\left(x-\dfrac{1}{2}\right)^3=-27\)
\(\Rightarrow\left(x-\dfrac{1}{2}\right)^3=\left(-3\right)^3\)
\(x-\dfrac{1}{2}=-3\)
\(x=-3+\dfrac{1}{2}\)
\(x=\dfrac{-5}{2}\)
d) 5 . 5x + 1 = 125
5x + 1 = 125 : 5
5x + 1 = 25
5x + 1 = 52
x + 1 = 2
x = 2 - 1
x = 1.
HN
10 tháng 7 2017
1. Tìm n, biết:
a) \(\dfrac{-32}{\left(-2\right)^n}=4\)
\(\Rightarrow\dfrac{\left(-2\right)^5}{\left(-2\right)^n}=\left(-2\right)^2\)
\(\Rightarrow\left(-2\right)^n.\left(-2\right)^2=\left(-2\right)^5\)
(-2)n + 2 = (-2)5
n + 2 = 5
n = 5 - 2
n = 3.
b) \(\dfrac{8}{2^n}=2\)
\(\Rightarrow\dfrac{2^3}{2^n}=2\)
\(\Rightarrow\) 2n . 2 = 23
n + 1 = 3
n = 3 - 1
n = 2.
c) \(\left(\dfrac{1}{2}\right)^{2n-1}=\dfrac{1}{8}\)
\(\Rightarrow\left(\dfrac{1}{2}\right)^{2n-1}=\left(\dfrac{1}{2}\right)^3\)
2n - 1 = 3
2n = 3 + 1
2n = 4
n = 4 : 2
n = 2.
2. Tính:
a) \(\left(\dfrac{1}{2}\right)^3.\left(\dfrac{1}{4}\right)^2\)
\(=\left(\dfrac{1}{2}\right)^3.\left[\left(\dfrac{1}{2}\right)^2\right]^2\)
\(=\left(\dfrac{1}{2}\right)^3.\left(\dfrac{1}{2}\right)^4\)
\(=\left(\dfrac{1}{2}\right)^7\)
\(=\dfrac{1}{128}\)
b) 273 : 93
= (33)3 : (32)3
= 39 : 36
= 33
= 27
c) 1252 : 253
= (53)2 : (52)3
= 56 : 56
= 1
d) \(\dfrac{27^2.8^5}{6^6.32^3}\)
\(=\dfrac{\left(3^3\right)^2.\left(2^3\right)^5}{6^6.\left(2^5\right)^3}\)
\(=\dfrac{3^6.2^{15}}{6^6.2^{15}}\)
\(=\dfrac{3^6}{6^6}\)
\(=\dfrac{1}{64}.\)
10 tháng 7 2017
B2 :
b) 27\(^3\): 9\(^3\)= (27:9)\(^3\)= 3\(^3\)
c) 125\(^2\): 25\(^3\)= 15625 : 15625 = 1
26 tháng 5 2022
a: \(=\left(\dfrac{-1}{3}:\dfrac{-2}{3}\right)^3+\left(\dfrac{4}{21}\cdot\dfrac{21}{4}\right)^{50}+0.01\)
\(=\left(\dfrac{1}{2}\right)^3+1^{50}+0.01=0.125+1+0.01=1.135\)
b: \(=x:y+\left(\dfrac{2x}{y}\right)^2-11x+12x-12y\)
\(=\dfrac{x}{y}+\dfrac{4x^2}{y^2}+x-12y\)
\(=\dfrac{x^2+4x^2+xy^2-12y^3}{y^2}=\dfrac{5x^2+xy^2-12y^3}{y^2}\)
3 tháng 8 2018
a) 27x : 3x = 9
(27 : 3)x = 9
9x = 91
x = 1
b) 25 : 5x =5
5x = 25 : 5
5x = 51
x = 1
c) 2 : (x + 2)2 = \(\dfrac{1}{18}\)
(x + 2)2 = 2 : \(\dfrac{1}{18}\)
(x + 2)2 = 36
\(\Rightarrow\left[{}\begin{matrix}x+2=6\\x+2=-6\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=4\\x=-8\end{matrix}\right.\)
d) (5x - 1)2 = \(\dfrac{36}{49}\)
(5x - 1)2 = \(\left(\dfrac{6}{7}\right)^2\)
Bạn làm tiếp nha, mình có việc bận :v
14 tháng 6 2017
a.
| x | = 5,6
=>\(\left[{}\begin{matrix}x=5,6\\x=-5,6\end{matrix}\right.\)
Vậy \(x\in\left\{-5,6;5,6\right\}\)
b, \(\left|x-3,5\right|=5\)
=>\(\left[{}\begin{matrix}x-3,5=5\\x-3,5=-5\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=8,5\\x=-1,5\end{matrix}\right.\)
Vậy \(x\in\left\{-1,5;8,5\right\}\)
c,\(\left|x-\dfrac{3}{4}\right|-\dfrac{1}{2}=0\)
=> \(\left|x-\dfrac{3}{4}\right|=\dfrac{1}{2}\)
=>\(\left[{}\begin{matrix}x-\dfrac{3}{4}=\dfrac{1}{2}\\x-\dfrac{3}{4}=-\dfrac{1}{2}\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}x=\dfrac{5}{4}\\x=\dfrac{1}{4}\end{matrix}\right.\)
Vậy \(x\in\left\{\dfrac{1}{4};\dfrac{5}{4}\right\}\)
d,\(\left|4x\right|-\left(\left|-13,5\right|\right)=\left|\dfrac{1}{4}\right|\)
=> \(\left|4x\right|-13,5=\dfrac{1}{4}\)
=> \(\left|4x\right|=13,75\)
=>\(\left[{}\begin{matrix}4x=13,75\\4x=-13,75\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=3,4375\\x=-3,4375\end{matrix}\right.\)
Vậy \(x\in\left\{-3,4375;3,4375\right\}\)
14 tháng 6 2017
e, ( x - 1 ) 3 = 27
=> x - 1 = 3
=> x = 4
Vậy x = 4
f, ( 2x - 3)2 = 36
=> \(\left[{}\begin{matrix}2x-3=6\\2x-3=-6\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}x=4,5\\x=-1,5\end{matrix}\right.\)
Vậy x\(\in\left\{-1,5;4,5\right\}\)
g, \(5^{x+2}=625\)
=> \(5^{x+2}=5^4\)
=> x + 2 = 4
=> x = 2
Vậy x = 2
h, ( 2x - 1)3 = -8
=> 2x - 1 = -2
=> x = \(\dfrac{-1}{2}\)
Vậy x = \(\dfrac{-1}{2}\)
i, \(\dfrac{1}{4}.\dfrac{2}{6}.\dfrac{3}{8}.\dfrac{4}{10}.\dfrac{5}{12}...\dfrac{30}{62}.\dfrac{31}{64}=2^x\)
=> \(\dfrac{1.2.3.4.5...30.31}{4.6.8.10.12...62.64}=2^x\)
=>\(\dfrac{1.2.3.4.5...30.31}{\left(2.3.4.5...30.31.32\right)\left(2.2.2.2...2.2_{ }\right)}=2^x\)(có 31 số 2)
=> \(\dfrac{1}{32.2^{31}}=2^x\)
=> \(\dfrac{1}{2^{36}}=2^x\)
=> x = -36
Vậy x = -36
TY
30 tháng 10 2018
a) Ta có: x : y : z = 2 : 3 : 5
⇒ \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{5}\)
Giả sử: \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{5}=k\)
⇒ x = 2k ; y = 3k ; z = 5k
Ta có: xyz = 810
⇒ 2k . 3k . 5k = 810
30 . k3 = 810
k3 = 810 : 30
k3 = 27
⇒ k = 3
⇒ k = 3 ⇒ x = 2 . 3 = 6
y = 3 . 3 = 9
z = 5 . 3 = 15
Vậy x = 6 ; y = 9 ; z = 15
b) Ta có: \(\dfrac{x^3}{8}=\dfrac{y^3}{27}=\dfrac{z^3}{64}\)
⇒ \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}\) ⇒ \(\dfrac{x^2}{4}=\dfrac{2y^2}{18}=\dfrac{3z^2}{48}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có
\(\dfrac{x^2}{4}=\dfrac{2y^2}{18}=\dfrac{3z^2}{48}=\dfrac{x^2+2y^2-3z^2}{4+18-48}\)
\(=\dfrac{-650}{-26}=25\)
+) \(\dfrac{x}{2}=25\) ⇒ x = 50
\(\dfrac{y}{3}=25\) ⇒ y = 75
\(\dfrac{z}{4}=25\) ⇒ z = 100
Vậy x = 50 ; y = 75 ; z = 100
(3x+21)3=\(\dfrac{27}{8}\)
\(\Rightarrow\)(3x+21)3=\(\left(\dfrac{3}{2}\right)^3\)
\(\Rightarrow\)3x+21=\(\dfrac{3}{2}\)
\(\Rightarrow\)3x =\(\dfrac{3}{2}\)-21=\(\dfrac{-39}{2}\)
\(\Rightarrow\)x =\(\dfrac{-39}{2}\):3
\(\Rightarrow\) =\(\dfrac{-13}{2}\)
Vậy x =\(\dfrac{-13}{2}\)
\(\left(3x+21\right)^3=\dfrac{27}{8}\)
\(\Rightarrow3x+3.7=\dfrac{1}{2}.3\)
\(\Rightarrow x+7=\dfrac{1}{2}\)
\(\Rightarrow x=-7\dfrac{1}{2}\)