Question

${x}^{2} - 81 = 0$
$49 {x}^{2} = 36$
${x}^{2} - 14 = 0$
${x}^{2} - 144 = 0$
​

Answer 1

$a)\\\\\\x^2-81~=~0\\\\\\x^2~=~81\\\\\\x~=~\pm\sqrt{81}\\\\\\\boxed{x~=~\pm9}\\\\\\S=\{\,x\in\mathbb{R}\,|\,~x=-9~ou~x=9\,\}$

$b)\\\\\\49x^2~=~36\\\\\\x^2~=~\frac{36}{49}\\\\\\x~=~\pm\sqrt{\frac{36}{49}}\\\\\\\boxed{x~=~\pm\frac{6}{7}}\\\\\\S=\{\,x\in\mathbb{R}\,|\,~x=-\frac{6}{7}~ou~x=\frac{6}{7}\,\}$

$c)\\\\\\x^2-14~=~0\\\\\\x^2~=~14\\\\\\\boxed{x~=~\pm\sqrt{14}}\\\\\\S=\{\,x\in\mathbb{R}\,|\,~x=-\sqrt{14}~ou~x=\sqrt{14}\,\}$

$d)\\\\\\x^2-144~=~0\\\\\\x^2~=~144\\\\\\x~=~\pm\sqrt{144}\\\\\\\boxed{x~=~\pm12}\\\\\\S=\{\,x\in\mathbb{R}\,|\,~x=-12~ou~x=12\,\}$