For n odd integer the following identity holds xn+yn=(x+y)(xn−1−xn−2y+⋯−xyn−2+yn−1) or xn+ynx+y=(xn−1−xn−2y+⋯−xyn−2+yn−1) He

Answer of this question

Solve (x^5+y^5)/x+y

Samira Singhania

For $n$ odd integer the following identity holds

$x^{n} + y^{n} = (x + y) (x^{n - 1} - x^{n - 2} y + \dots - x y^{n - 2} + y^{n - 1})$

$\frac{x^{n} + y^{n}}{x + y} = (x^{n - 1} - x^{n - 2} y + \dots - x y^{n - 2} + y^{n - 1})$

Hence for our case we have that

$\frac{x^{5} + y^{5}}{x + y} = x^{4} - x^{3} y + x^{2} y^{2} - x y^{3} + y^{4}$

Written on Jan. 27, 2018, 10:35 a.m.

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Class 6