Question

tìm quan hệ x và y biết

x\(^4\)=y\(^4\)

x\(^5\)=y\(^5\)

Answer 1

Ta có: 

\(x^4=y^4\)

\(\Rightarrow x^4-y^4=0\)

\(\Rightarrow\left(x^2\right)^2-\left(y^2\right)^2=0\)

\(\Rightarrow\left(x^2-y^2\right)\left(x^2+y^2\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x^2-y^2=0\\x^2+y^2=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x-y=0\\x+y=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=y\\x=-y\end{matrix}\right.\)

_______________

Ta có: 

\(x^5=y^5\)

\(\Rightarrow x^5-y^5=0\)

\(\Rightarrow x-y=0\)

\(\Rightarrow x=y\)