Giải thích các bước giải:

Ta có:

\(\begin{array}{l}
a,\\
{\left( {2x - 3} \right)^2} + 75 = 100\\
 \Leftrightarrow {\left( {2x - 3} \right)^2} = 100 - 75\\
 \Leftrightarrow {\left( {2x - 3} \right)^2} = 25\\
 \Leftrightarrow {\left( {2x - 3} \right)^2} = {5^2}\\
 \Leftrightarrow 2x - 3 = 5\\
 \Leftrightarrow 2x = 5 + 3\\
 \Leftrightarrow 2x = 8\\
 \Leftrightarrow x = 8:2\\
 \Leftrightarrow x = 4\\
b,\\
5x - 35 = 25\\
 \Leftrightarrow 5x = 25 + 35\\
 \Leftrightarrow 5x = 60\\
 \Leftrightarrow x = 60:5\\
 \Leftrightarrow x = 12\\
c,\\
{\left( {3x - 5} \right)^2} - 18 = 31\\
 \Leftrightarrow {\left( {3x - 5} \right)^2} = 31 + 18\\
 \Leftrightarrow {\left( {3x - 5} \right)^2} = 49\\
 \Leftrightarrow {\left( {3x - 5} \right)^2} = {7^2}\\
 \Leftrightarrow 3x - 5 = 7\\
 \Leftrightarrow 3x = 7 + 5\\
 \Leftrightarrow 3x = 12\\
 \Leftrightarrow x = 12:3\\
 \Leftrightarrow x = 4
\end{array}\) 

Đáp án:

a ) \(\left[ \begin{array}{l}x=4\\x=-1\end{array} \right.\)

b ) x = 12

c ) \(\left[ \begin{array}{l}x=4\\x=-\frac{2}{3}\end{array} \right.\) 

Giải thích các bước giải:

a ) $(2x-3)^{2}$ + 75 = 100

→ $(2x-3)^{2}$ = 25

→ \(\left[ \begin{array}{l}(2x-3)^2=5^2\\(2x-3)^2=(-5)^2\end{array} \right.\)

→ \(\left[ \begin{array}{l}2x-3=5\\2x-3=-5\end{array} \right.\)

→ \(\left[ \begin{array}{l}2x=8\\2x=-2\end{array} \right.\)

→ \(\left[ \begin{array}{l}x=4\\x=-1\end{array} \right.\)

b ) 5x - 35 = 25

→ 5x = 60

→ x = 12

c ) $(3x-5)^{2}$ - 18 = 31

→ $(3x-5)^{2}$ = 49

→ \(\left[ \begin{array}{l}(3x-5)^2=7^2\\(3x-5)^2=(-7)^2\end{array} \right.\) 

→ \(\left[ \begin{array}{l}3x-5=7\\3x-5=-7\end{array} \right.\) 

→ \(\left[ \begin{array}{l}3x=12\\3x=-2\end{array} \right.\) 

→ \(\left[ \begin{array}{l}x=4\\x=-\frac{2}{3}\end{array} \right.\)