Question

Cho A= \(\left(-3x^5y^3\right)^4\); B=\(\left(2x^2z^4\right)^5\)

Tìm x; y; z biết A+B=0

Answer 1

Ta có :

A=\(\left(-3x^5y^3\right)^4\ge0\forall x,y\)

B=\(\left(2x^2z^4\right)^5=\left(2xz^2\right)^{10}\ge0\forall x,z\)

Mà A+B = 0

\(\Rightarrow\left\{{}\begin{matrix}A=0\\B=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-3x^5y^3\\2xz^2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left\{{}\begin{matrix}x=0\\y=0\end{matrix}\right.\\\left\{{}\begin{matrix}x=0\\z=0\end{matrix}\right.\end{matrix}\right.\)

Vậy x =0 ; y = 0 ; z = 0 là các giá trị cần tìm