Question

Giải hệ phương trình

\(\left\{{}\begin{matrix}2y^3+7y+2x\sqrt{1-x}=3\sqrt{1-x}+3\left(2y^2+1\right)\\\sqrt{2y^2-4y+3}=5-y+\sqrt{x+4}\end{matrix}\right.\)

Answer 1

ĐKXĐ: ...

\(2\left(y^3-3y^2+3y-1\right)+y-1=\left(1+2\left(1-x\right)\right)\sqrt{1-x}\)

\(\Leftrightarrow2\left(y-1\right)^3+\left(y-1\right)=2\sqrt{1-x}^3+\sqrt{1-x}\)

Đặt \(\left\{{}\begin{matrix}y-1=a\\\sqrt{1-x}=b\end{matrix}\right.\)

\(\Leftrightarrow2a^3+a=2b^3+b\Leftrightarrow\left(a-b\right)\left(2a^2+2ab+2b^2+1\right)=0\)

\(\Leftrightarrow a=b\Leftrightarrow y-1=\sqrt{1-x}\) (\(y\ge1\))

\(\Leftrightarrow\left(y-1\right)^2=1-x\)

\(\Leftrightarrow\sqrt{2\left(y-1\right)^2+1}=5-1-\sqrt{1-x}+\sqrt{x+4}\)

\(\Leftrightarrow\sqrt{2\left(1-x\right)+1}=4-\sqrt{1-x}+\sqrt{x+4}\)

\(\Leftrightarrow...\)