Câu hỏi của Nguyễn Thị Thanh Trang

Question

Giải phương trình: $\frac{1}{x+1}+\frac{2}{1+\sqrt{x}}=\frac{2+\sqrt{x}}{2x}$

Help me ;D

B.Thị Anh Thơ · Accepted Answer

Đặt $\sqrt{x}=t\left(t>0\right)$

$\Leftrightarrow\frac{1}{1+t^2}+\frac{2}{1+t}=\frac{2+t}{2t^2}$

$\Leftrightarrow\frac{1+t+2t+2t^2}{\left(1+t\right)\left(1+t^2\right)}=\frac{2+t}{2t^2}$

$\Leftrightarrow\frac{2t^2+3t+1}{\left(1+t\right)\left(1+t^2\right)}=\frac{2+t}{2t^2}$

$\Leftrightarrow\frac{\left(t+1\right)\left(2t+1\right)}{\left(1+t\right)\left(1+t^2\right)}=\frac{2+t}{2t^2}$

$\Leftrightarrow\frac{2t+1}{1+t^2}=\frac{2+t}{2t^2}$

$\Leftrightarrow2t^2\left(2t+1\right)=\left(2-t\right)\left(1+t^2\right)$

$\Leftrightarrow4t^3+2t^2=2+2t^2+1+t^3$

$\Leftrightarrow t=1$

$\Leftrightarrow\sqrt{x}=1$

$\Leftrightarrow x=1$Câu trả lời: Đặt $\sqrt{x}=t\left(t>0\right)$