Đáp án:
$a, S=\{25\}$
$b,S=\{227\}$
$c,S=\{9\}$
Giải thích các bước giải:
a) ĐKXĐ: $x\ge 0$
$3\sqrt x=\sqrt{16x}-5$
$⇔3\sqrt{x}-4\sqrt x=-5$
$⇔-\sqrt x=-5$
$⇔\sqrt x=5$
$⇔x=25\,(TM)$
Vậy $S=\{25\}$
b) ĐKXĐ: $x\ge 2$
$\sqrt{4x-8}-\sqrt{9x-8}+4\sqrt{\dfrac{x-2}{25}}=-3$
$⇔2\sqrt{x-2}-3\sqrt{x-2}+\dfrac{4}{5}\sqrt{x-2}=-3$
$⇔-\dfrac{1}{5}\sqrt{x-2}=-3$
$⇔\sqrt{x-2}=15$
$⇔x-2=225$
$⇔x=227\,(TM)$
Vậy $S=\{227\}$
c) ĐKXĐ: $x\ge -\dfrac{4}{5}$
$x-\sqrt{5x+4}=2$
$⇔\sqrt{5x+4}=x-2$
$⇔5x+4=(x-2)^2\,\,(ĐK:x\ge 2)$
$⇔5x+4=x^2-4x+4$
$⇔x^2-9x=0$
$⇔x(x-9)=0$
$⇔\left[ \begin{array}{l}x=0\,(L)\\x=9\end{array} \right.$
Vậy $S=\{9\}$.
