Question

1) x\(^3\) + y\(^3\) = 19

2) (x + y)(8 + y) = 2

3) \(\left\{{}\begin{matrix}x+y+\sqrt{xy}=19\\x^2+2y^2+xy=133\end{matrix}\right.\)

4) \(\left\{{}\begin{matrix}\sqrt[4]{y^3-1}+\sqrt{x}=3\\x^2+y^3=82\end{matrix}\right.\)

Answer 1

ĐKXĐ: \(x\ge0;y\ge1\).

Đặt \(\left\{{}\begin{matrix}\sqrt[4]{y^3-1}=a\ge0\\\sqrt{x}=b\ge0\end{matrix}\right.\).

HPT đã cho trở thành:

\(\left\{{}\begin{matrix}a+b=3\\a^4+b^4=81\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}a+b=3\\\left(a+b\right)^4-2ab\left(2a^2+3ab+2b^2\right)=81\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}a+b=3\\ab\left(2a^2+3ab+2b^2\right)=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}a=3;b=0\\a=0;b=3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=9;y=1\\x=0;y=\sqrt[3]{82}\end{matrix}\right.\).