Question

Cho số thực a,b,x,y thỏa mãn a+b=x+y và\(a^2+b^2=x^2+y^2\)

CMR \(a^{2017}+b^{2017}=x^{2017}+y^{2017}\)

Answer 1

Bài làm

a+b=x+y=>a²+2ab+b²=x²+2xy+y²=>2ab=2xy=>a²-2ab+b²

=x²-2xy+y²=>(a+b)²=(x-y)²⁼>\(\orbr{\begin{cases}a-b=x-y\\a-b=y-x\end{cases}}\)

\(+,a-b=x-y\Rightarrow a+b-\left(a-b\right)=x+y-\left(x-y\right)\Rightarrow2a=2x\Rightarrow a=x\Rightarrow b=y\)

\(\Rightarrow a^{2017}+b^{2017}=x^{2017}+y^{2017}\)

\(+,a-b=y-x\Rightarrow\left(a+b\right)+\left(a-b\right)=x+y+\left(y-x\right)\Rightarrow2a=2y\Rightarrow a=y\Rightarrow b=x\)

\(=x\Rightarrow a^{2017}+b^{2017}=x^{2017}+y^{2017}\Rightarrow\left(đpcm\right)\)

Answer 2

Ê, giẻ rách, mày copy vừa thôi