Question

giải hệ phương trỉnh

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

Answer 1

\(\Rightarrow2x^3-\left(x^3+y^3\right)=5y-5x\)

\(\Leftrightarrow x^3-y^3+5\left(x-y\right)=0\)

\(\Leftrightarrow\left(x-y\right)\left(x^2+xy+y^2+5\right)=0\)

\(\Leftrightarrow x=y\)

Thay vào pt sau: \(2x^3=1\Rightarrow x=y=\frac{1}{\sqrt[3]{2}}\)