Đáp án:
$\dfrac{36}{x+2} + \dfrac{36}{x-2} = 4,5$
$\text{ĐKXĐ : $x \neq ± 2 $}$
$⇒36(x-2) + 36(x+2) = 4,5(x-2)(x+2)$
$⇔36x - 72 +36x +72 = 4,5x^2+9x -9x -18$
$⇔4,5x^2-72x -18=0$
$⇔x^2-16x-4=0$
$⇔x^2 -2.x.8 + (8)^2 -68 =0$
$⇔(x-8)^2-68=0$
$⇔(x-8 -\sqrt[]{68}).(x-8+\sqrt[]{68})=0$
$⇔$\(\left[ \begin{array}{l}x-8-\sqrt[]{68}=0\\x-8+\sqrt[]{68}=0\end{array} \right.\)
$⇔$\(\left[ \begin{array}{l}x=8+2\sqrt[]{17}(TM)\\x=8-2\sqrt[]{17}(TM)\end{array} \right.\)
$\text{Vậy S={$8+2\sqrt[]{17} ; 8-2\sqrt[]{17}$}}$
