`a)` `96:3-` $x^{2}$ `=7`

`32-` $x^{2}$ `=7`

$x^{2}$ `=32-7`

$x^{2}$ `=25`

$x^{2}$ `=` $5^{2}$

`=>` `x=±5`

Vậy `x=±5`

`b)` $(x-3)^{2}$ `=` $15^{2}$ `-` $12^{2}$

$(x-3)^{2}$ `=225-144`

$(x-3)^{2}$ `=81`

$(x-3)^{2}$ `=$9^{2}$`

`=>` \(\left[ \begin{array}{l}x-3=9\\x-3=-9\end{array} \right.\)

`=>` \(\left[ \begin{array}{l}x=9+3\\x=-9+3\end{array} \right.\)

`=>` \(\left[ \begin{array}{l}x=12\\x=-6\end{array} \right.\) 

Vậy `x∈{12; -6}`

`c)` `(18-` $x^{3}$`).5=50`

`18-` $x^{3}$ `=50:5`

`18-` $x^{3}$ `=10`

$x^{3}$ `=18-10`

$x^{3}$ `=8`

$x^{3}$ `=` $2^{3}$

`=>x=2`

Vậy `x=2`

`d)` $(2x+13)^{3}$ `=125`

$(2x+13)^{3}$ `=` $5^{3}$

`=>2x+13=5`

`2x=5-13`

`2x=-8`

`x=-8:2`

`x=-4`

Vậy `x=-4`

`e)` $5^{x+2}$ `=602+23`

$5^{x+2}$ `=625`

$5^{x+2}$ `=` $5^{4}$

`=>x+2=4`

`x=4-2`

`x=2`

Vậy `x=2`

`f)` $2^{x+5}$ `.128=1024`

$2^{x+5}$ `=1024:128`

$2^{x+5}$ `=8`

$2^{x+5}$ `=` $2^{3}$

`=>x+5=3`

`x=3-5`

`x=-2`

Vậy `x=-2`

Đáp án:

$\displaystyle \begin{array}{{>{\displaystyle}l}} a.x=\pm 5\\ b.x=12\ hoặc\ x=-6\\ c.x=2\\ d.x=-4\\ e.x=2\\ f.x=-2 \end{array}$

Giải thích các bước giải:

$\displaystyle \begin{array}{{>{\displaystyle}l}} a.96:3-x^{2} =7\\ \Leftrightarrow -x^{2} =7-32=-25\\ \Leftrightarrow x^{2} =25\Leftrightarrow x=\pm 5\\ b.\ ( x-3)^{2} =15^{2} -12^{2}\\ \Leftrightarrow x^{2} -6x+9-81=0\\ \Leftrightarrow x^{2} -6x-72=0\\ \Leftrightarrow x^{2} -12x+6x-72=0\\ \Leftrightarrow ( x-12)( x+6) =0\\ \Leftrightarrow x=12\ hoặc\ x=-6\\ c.\ \left( 18-x^{3}\right) .5=50\\ \Leftrightarrow 18-x^{3} =10\\ \Leftrightarrow x^{3} =8\\ \Leftrightarrow x=2\\ d.\ ( 2x+13)^{3} =125\\ \Leftrightarrow 2x+13=5\\ \Leftrightarrow x=-4\\ e.\ 5^{x+2} -23=602\\ \Leftrightarrow 5^{x+2} =625=5^{4}\\ \Leftrightarrow x+2=4\Leftrightarrow x=2\\ f.\ 2^{x+5} .128=1024\\ \Leftrightarrow 2^{x+5} =8=2^{3}\\ \Leftrightarrow x+5=3\Leftrightarrow x=-2 \end{array}$