Question

Giải pt x + 4 căn x + 3 + 2 căn 3 - 2x = 11

Answer 1

ĐKXĐ: \(\begin{cases}x+3\ge0\\ 3-2x\ge0\end{cases}\Rightarrow\begin{cases}x\ge-3\\ 2x\le3\end{cases}\Rightarrow-3\le x\le\frac32\)

\(x+4\sqrt{x+3}+2\sqrt{3-2x}=11\)

=>\(x-1+4\sqrt{x+3}-8+2\sqrt{3-2x}-2=0\)

=>\(x-1+4\cdot\left(\sqrt{x+3}-2\right)+2\left(\sqrt{3-2x}-1\right)=0\)

=>\(x-1+4\cdot\frac{x+3-4}{\sqrt{x+3}+2}+2\cdot\frac{3-2x-1}{\sqrt{3-2x}+1}=0\)

=>\(x-1+4\cdot\frac{x-1}{\sqrt{x+3}+2}+2\cdot\frac{-2x+2}{\sqrt{3-2x}+1}=0\)

=>\(\left(x-1\right)\left(1+\frac{4}{\sqrt{x+3}+2}-\frac{4}{\sqrt{3-2x}+1}\right)=0\)

=>x-1=0

=>x=1(nhận)