Question

prove that a^3+b^3>a^2b+ab^2​

Answer 1

a3+b3 >a2b + ab2

a3+b3>ab(a+b)

(a+b)(a2+b2+ab)>ab(a+b)

divide both side by (a+b)

then we get

a2+b2+ab>ab

subtract ab from both side

we get

a2+b2>0

so hence it is proved

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