Đáp án:
Giải thích các bước giải:
(($\sqrt[]{x+3}$ -$\sqrt[]{x+1}$ )($x^{2}$ +$\sqrt[]{}$ $x^{2}$ +4x+3 )=2x
($\sqrt[]{x+3}$ $\sqrt[]{x+1}$ )($x^{2}$ +$\sqrt[]{(x+3)(x+1)}$ )=2xĐặt $\sqrt[]{x+3}$ =a(a>0) $\sqrt[]{x+1}$ =b(b>0)
⇒(a-b)($x^{2}$ +ab)=2x
⇔ax²+a²b-bx²-ab²-2x=0
⇔ax²-bx²-2x=0 (a²b=ab² nha)
⇔x(ax-bx-2)=0
ax-bx-2=0
⇔x(a-b)-2=0
⇒x($\sqrt[]{x+3}$ -$\sqrt[]{x+1}$ )-2=0
⇔[x($\sqrt[]{x+3}$ -$\sqrt[]{x+1}$ )]²=2²
⇔x²(x+3-x-1)=4
⇔2x²-4=0
⇔\(\left[ \begin{array}{l}x=√2\\x=-√2\end{array} \right.\)
Vậy S={√2;-√2}
