Question

(x^n+y^n)/(x^n-1+y^n-1)=(xy)^1/2 then n=?

Answer 1

here this answer


xn−yn=(x−y)(xn−1+xn−2y+⋯+xyn−2+yn−1)=x⋅xn−1+x⋅xn−2⋅y+⋯+x⋅x⋅yn−2+x⋅yn−1+(−y)⋅xn−1+(−y)⋅xn−2⋅y+⋯+(−y)⋅x⋅yn−2+(−y)⋅yn−1=xn+xn−1y+⋯+x2yn−2+xyn−1−xn−1y−y2xn−2−⋯−xyn−1−yn=xn+x2yn−2−xn−2y2−yn≠xn−ynxn−yn=(x−y)(xn−1+xn−2y+⋯+xyn−2+yn−1)=x⋅xn−1+x⋅xn−2⋅y+⋯+x⋅x⋅yn−2+x⋅yn−1+(−y)⋅xn−1+(−y)⋅xn−2⋅y+⋯+(−y)⋅x⋅yn−2+(−y)⋅yn−1=xn+xn−1y+⋯+x2yn−2+xyn−1−xn−1y−y2xn−2−⋯−xyn−1−yn=xn+x2yn−2−xn−2y2−yn≠xn−yn

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