\(\frac{2x-10}{6}=\frac{-27}{5-x}\)

\(\frac{2\left(x-5\right)}{6}=\frac{27}{x-5}\)

\(2\left(x-5\right)^2=27\times6\)

\(2x^2-20x+50-162=0\)

\(2x^2-20x-112=0\)

\(x^2-10x-56=0\)

\(x^2-14x+4x-56=0\)

\(\left(x-14\right)\left(x+4\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-14=0\\x+4=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=14\\x=-4\end{cases}}\)

KL .....

XIN TIICK

|x - 5| = |-7|

=> |x - 5| = 7

=> \(\orbr{\begin{cases}x-5=7\\x-5=-7\end{cases}}\)

=> \(\orbr{\begin{cases}x=12\\x=-2\end{cases}}\)

c ) | x - 5 | = | -7 |

cs 2 trường hợp

TH1 x-5=7

x=5+7

x=12

TH2 x-5=-7

x=-7+5

x=-2

# chi kute@#

| x -5 | = | -7 |

=> | x-5 | = \(\pm\)7

=>\(\orbr{\begin{cases}\left|x-5\right|=-7\\\left|x-5\right|=7\end{cases}}\)

=> \(\orbr{\begin{cases}\left|x\right|=-7+5\\\left|x\right|=7+5\end{cases}}\)

=> \(\orbr{\begin{cases}x=-2\\x=12\end{cases}}\)

Đề trước đó: 

(x-7)(x+1)-(x-3)^2=(3x-5)(3x+5)-(3x+1)^2+(x-2)^2-x

<=>x^2+x-7x-7-x^2+6x-9=9x^2-25-9x^2-6x-1+x^2-4x+4-x

<=>x^2-11x-6=0

<=>x^2-2x. 11/2 + 121/4-145/4=0

<=>(x-11/2)^2=145/4

<=>|x-11/2|=căn(145)/2

<=>x=[11+-căn(145)]/2

a) (426 + x) : 5 = 120

(=) 426 + x = 120 :5

(=) 426 + x = 24

(=) x = 24 - 426

(=) x = - 402

Vậy x = - 402

b) 5844 : x -159 = 328

(=) 5844 : x = 328+ 159

(=) 5844 : x = 487

(=) x = 5844 : 487

(=) x = 12

Vậy x = 12

 c) 3^2x + 1 = 27 

(=) 3^2x = 27 -1 

(=) 3^2x = 26 

=> vô lý 

vậy x thuộc tập hợp rỗng

d) (3x - 1)² = 64

(=) (3x - 1)² = 8²

(=) 3x - 1 = 8

(=) 3x = 8 + 1

(=) 3x = 9

(=) x = 9 : 3

(=) x = 3

Vậy x = 3

( 426 + x ) : 5 = 120

( 426 + x ) = 600

           x   = 600 - 426

           x  = 174

b ) 5844 : x - 159 = 328

     5844 : x         = 328 + 159

     5844 : x         = 487

               x         = 5844 : 487

               x          = 12

d ) ( 3x - 1 ) ² = 64

     ( 3x - 1 ) = 8

       3x        = 9

         x       = 3

\(\left(426+x\right):5=120\)

\(\Rightarrow\left(460+x\right)=600\)

\(\Rightarrow x=600-426\)

\(\Rightarrow x=174\)

Ta có :\(\hept{\begin{cases}-2x-11:3x+2\\3x+2:3x+2\end{cases}}\)\(​​​​\implies\)\(\hept{\begin{cases}3.\left(-2x-11\right):3x+2\\2\left(3x+2\right):3x+2\end{cases}}\) \(\implies\) \(\hept{\begin{cases}-6x-33:3x+2\\6x+4:3x+2\end{cases}}\)

  \(\implies\)    \(-6x-33+6x+4:3x+2\) 

  \(\implies\)    \(-29:3x+2\)

  \(\implies\)    \(3x+2\) \(\in\)  Ư(-29)=\(\{\)\(1;-1;29;-29\) \(\}\)

  \(\implies\)  \(x\) \(\in\) \(\{\) \(-1;9\)\(\}\)

\(\Leftrightarrow\left\{{}\begin{matrix}8x-20y=44\\15x+20y=25\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=-1\end{matrix}\right.\)

a) \(\left(x-\frac{1}{2}\right)^4=\frac{1}{81}\)

\(\Rightarrow\left(x-\frac{1}{2}\right)^4=\left(\frac{1}{3}\right)^4\)

\(\Rightarrow\orbr{\begin{cases}x-\frac{1}{2}=\frac{1}{3}\\x-\frac{1}{2}=\frac{-1}{3}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{5}{6}\\x=\frac{1}{6}\end{cases}}\)

Vậy ...

trả lời

\(x=\frac{1}{6}\)

hk tốt

b) ta có: \(5^{50}=\left(5^2\right)^{25}=25^{25}\); \(3^{75}=\left(3^3\right)^{25}=27^{25}\).

Mà \(25^{25}< 27^{25}\)nên \(5^{50}< 3^{75}\)