tìm x trong các tỉ lệ thức
\(\frac{x-1}{x+5}\)=\(\frac{6}{7}\) ; \(\frac{x^2}{6}\)= \(\frac{24}{25}\) ; \(\frac{x-2}{x-1}\) = \(\frac{x+4}{x+7}\)
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QT
1
23 tháng 8 2021
a, \(\frac{x-6}{x+4}=\frac{2}{7}\Rightarrow7x-42=2x+8\)ĐK : \(x\ne-4\)
\(\Leftrightarrow5x=50\Leftrightarrow x=10\)(tm)
b, \(\left(x+5\right):2\frac{1}{2}=\frac{40}{x+5}\)ĐK : \(x\ne-5\)
\(\Leftrightarrow\frac{5\left(x+5\right)}{2}=\frac{40}{x+5}\Rightarrow5\left(x+5\right)^2=80\Leftrightarrow\left(x+5\right)^2=16\)
TH1 : \(x+5=4\Leftrightarrow x=-1\)
TH2 : \(x+5=-4\Leftrightarrow x=-9\)
LH
28 tháng 9 2017
a) \(\frac{x-1}{x+5}=\frac{6}{7}\)
7( x - 1 ) = 6( x + 5 )
7x - 7 = 6x - 30
7x - 6x = -30 + 7
x = -23
b) \(\frac{x^2}{6}=\frac{24}{25}\)
\(x^2.25=6.24\)
\(x^2.25=144\)
\(x^2=\frac{144}{25}\)
\(x=\sqrt{\frac{144}{25}}\)
\(x=\frac{12}{5}\)
c) \(\frac{x-2}{x-4}=\frac{x+4}{x+7}\)
\(\left(x-2\right)\left(x+7\right)=\left(x+4\right)\left(x-4\right)\)
\(x^2+7x-2x-14=x^2-4x+4x-16\)
\(x^2+5x-14=x^2^{ }-16\)
\(x^2-x^2+5x=-16+14\)
\(5x=-2\)\(x=\frac{-2}{5}\)
12 tháng 11 2016
a) \(\frac{3x-2}{1\frac{2}{5}}=\frac{2\frac{3}{7}}{2\frac{3}{5}}\Rightarrow3x-2=1.\frac{2}{5}.\frac{2\frac{3}{7}}{2\frac{3}{5}}=\frac{7}{5}.\frac{17}{7}.\frac{5}{13}\)
\(3x-2=\frac{17}{13}\Rightarrow3x=2+\frac{17}{13}=\frac{43}{13}\Rightarrow x=\frac{43}{39}.\)
b) \(\frac{x}{0,16}=\frac{9}{x}\Rightarrow x^2=9.0,16=1,44\Rightarrow x=\pm1,2\)
TT
1
DN
1
29 tháng 2 2020
Ta có: \(\frac{x-1}{x+5}=\frac{6}{7}\)
⇔\(\left(x-1\right)\cdot7=6\left(x+5\right)\)
\(\Leftrightarrow7x-7=6x+30\)
\(\Leftrightarrow7x-7-6x-30=0\)
\(\Leftrightarrow x-37=0\)
hay x=37
Vậy: x=37
HQ
Hà Quang Minh
Giáo viên
16 tháng 9 2023
\(\begin{array}{l}a)\frac{x}{{ - 3}} = \frac{7}{{0,75}}\\ \Rightarrow x.0,75 = ( - 3).7\\ \Rightarrow x = \frac{{( - 3).7}}{{0,75}} = - 28\end{array}\)
Vậy x = 28
\(\begin{array}{l}b) - 0,52:x = \sqrt {1,96} :( - 1,5)\\ - 0,52:x = 1,4:( - 1,5)\\ x = \dfrac{(-0,52).(-1,5)}{1,4}\\x = \frac{39}{{70}}\end{array}\)
Vậy x = \(\frac{39}{{70}}\)
\(\begin{array}{l}c)x:\sqrt 5 = \sqrt 5 :x\\ \Leftrightarrow \frac{x}{{\sqrt 5 }} = \frac{{\sqrt 5 }}{x}\\ \Rightarrow x.x = \sqrt 5 .\sqrt 5 \\ \Leftrightarrow {x^2} = 5\\ \Leftrightarrow \left[ {_{x = - \sqrt 5 }^{x = \sqrt 5 }} \right.\end{array}\)
Vậy x \( \in \{ \sqrt 5 ; - \sqrt 5 \} \)
Chú ý:
Nếu \({x^2} = a(a > 0)\) thì x = \(\sqrt a \) hoặc x = -\(\sqrt a \)
16 tháng 9 2023
a: \(\dfrac{x}{-3}=\dfrac{7}{0.75}=\dfrac{28}{3}\)
=>\(x=\dfrac{28\left(-3\right)}{3}=-28\)
b: \(-\dfrac{0.52}{x}=\dfrac{\sqrt{1.96}}{-1.5}=\dfrac{1.4}{-1.5}\)
=>\(x=0.52\cdot\dfrac{1.5}{1.4}=\dfrac{39}{70}\)
c: \(\dfrac{x}{\sqrt{5}}=\dfrac{\sqrt{5}}{x}\)
=>\(x^2=5\)
=>\(x=\pm\sqrt{5}\)
25 tháng 9 2017
a) \(\frac{x}{7}=\frac{18}{14}\)
\(\frac{x}{7}=\frac{9}{7}\)
\(\Rightarrow x=9\)
b) \(6:x=1\frac{3}{4}:5\)
\(6:x=\frac{7}{4}.\frac{1}{5}\)
\(6:x=\frac{7}{20}\)
\(x=6:\frac{7}{20}\)
\(x=\frac{120}{7}\)
vay \(x=\frac{120}{7}\)
c) \(\frac{5,7}{0,35}=\frac{-x}{0,45}\)
\(\Rightarrow-0,35x=5,7.0,45\)
\(\Rightarrow-0,35x=2,565\)
\(\Rightarrow x=\frac{-2,565}{0,35}\)
\(\Rightarrow x=\frac{-513}{70}\)
vay \(x=\frac{-513}{70}\)
HT
4
13 tháng 10 2015
7.(x-1)= 5.(x+5)
7.x-7. = 5.x+25
7.x -5.x =25+7
2.x. = 32
x = 32:2
x. = 16
a) \(\frac{x-1}{x+5}=\frac{6}{7}\)
\(\Rightarrow7.\left(x-1\right)=6.\left(x+5\right)\)
\(\Rightarrow7x-7=6x+30\)
\(\Rightarrow7x-6x=7+30\)
\(\Rightarrow x=37\)
b) \(\frac{x^2}{6}=\frac{24}{25}\)
\(\Rightarrow25.x^2=24.6\)
\(\Rightarrow25.x^2=144\)
\(\Rightarrow x^2=144:25\)
\(\Rightarrow x^2=\frac{144}{25}\)
\(\Rightarrow x^2=\frac{12^2}{5^2}\)
\(\Rightarrow x^2=\frac{12}{5}^2\)
\(\Rightarrow x=\pm\frac{12}{5}\)
\(c,\frac{x-2}{x-1}=\frac{x+4}{x+7}\)
\(\Leftrightarrow(x-2)(x+7)=(x+4)(x-1)\)
\(\Leftrightarrow x^2+5x-14=x^2+3x-4\)
\(\Leftrightarrow x^2+5x-14-x^2+3x=-4\)
\(\Leftrightarrow\left[x^2-x^2\right]+5x-3x-14=-4\)
\(\Leftrightarrow2x-14=-4\)
\(\Leftrightarrow2x=10\Leftrightarrow x=5\)