Algebra

[Khushi Sharma]

Let a,b and c be real numbers  such that $a+b+c=0$ Prove that $\frac {a^5+b^5+c^5 }{5}=(\frac{a^3+b^3+c^3}{2})(\frac{a^2+b^2+c^2}{2}) $

[Cheenta Stat]

Hint 0: We have to generalised bothR.h.s and L.h.s

Hint 1 : Take C=-(a+b)

Hint 2: Now do binomial expansion for powers of 5 and 3

Hint 3: Now equate the coefficients of powers of a^i* b^j on R.h.s and L.h.s you will find that they are equal .

Hence done!

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