Đáp án:
`đpcm`
Giải thích các bước giải:
Từ `a^2+b^2=x^2+y^2`
`=> a^2-x^2=y^2-b^2`
`=> (a-x)(a+x)=(y-b)(a-x)`
`=> (a-x)(a+x)-(y-b)(a-x)=0`
`=> (a-x)(a+x-y+b)=0`
`=>` \(\left[ \begin{array}{l}a-x=0\\a+x-y+b=0\end{array} \right.\)
`=>` \(\left[ \begin{array}{l}a=x\\a+x=y+b\end{array} \right.\)
Khi `a=x; a+b=x+y`
`=> b=y`
`=> a^{2010} + b^{2010} = x^{2010} + y^{2010}`
Khi `a+x=y+b`; `a+b=x+y`
`=> a=y; b=x`
`=> a^{2010} + b^{2010} = x^{2010} + y^{2010}`