\(đk:x\ge-1\)
\(< =>x+1-2\sqrt{\left(x+1\right)\left(2x+3\right)}+2x+3=4-4x+x^2\)
\(< =>4\left(x+1\right)\left(2x+3\right)=\left(x^2-7x\right)^2\)
\(< =>8x^2+12x+8x+12=x^4-14x^3+49x^2\)
\(< =>x^4-14x^3+41x^2-20x-12=0\)
\(< =>\left(x-3\right)\left(x^3-11x^2+8x+4\right)=0\)
\(< =>\left[{}\begin{matrix}x=3\left(tm\right)\\x^3-11x^2+8x+4=0\left(1\right)\end{matrix}\right.\)
đến (1) chịu , =>x=3
ĐKXĐ: \(x\ge-1\)
\(\sqrt{x+1}-2+x-\sqrt{2x+3}=0\)
\(\Leftrightarrow\dfrac{x-3}{\sqrt{x+1}+2}+\dfrac{x^2-2x-3}{x+\sqrt{2x+3}}=0\)
\(\Leftrightarrow\dfrac{x-3}{\sqrt{x+1}+2}+\dfrac{\left(x+1\right)\left(x-3\right)}{x+\sqrt{2x+3}}=0\)
\(\Leftrightarrow\left(x-3\right)\left(\dfrac{1}{\sqrt{x+1}+2}+\dfrac{x+1}{x+\sqrt{2x+3}}\right)=0\)
\(\Leftrightarrow x-3=0\)
\(\Leftrightarrow x=3\)
