if-a-b-c-Prove-that-a-2-3-b-2-3-gt-c-2-3-Help-me-please-

Question Number 126144 by Ndala last updated on 17/Dec/20

i f : a + b = c

P r o v e t h a t : a^{\frac{2}{3}} + b^{\frac{2}{3}} > c^{\frac{2}{3}}

.

H e l p m e, p l e a s e!

Answered by MJS_new last updated on 18/Dec/20

a^{2 / 3} + b^{2 / 3} > {(a + b)}^{2 / 3}

{(a^{2 / 3} + b^{2 / 3})}^{3} > {(a + b)}^{2}

a^{2} + 3 a^{4 / 3} b^{2 / 3} + 3 a^{2 / 3} b^{4 / 3} + b^{2} > a^{2} + 2 a b + b^{2}

3 a^{2 / 3} b^{2 / 3} (a^{2 / 3} + b^{2 / 3}) > 2 a b

3 (a^{2 / 3} + b^{2 / 3}) > 2 a^{1 / 3} b^{1 / 3}

a^{2 / 3} - \frac{2}{3} a^{1 / 3} b^{1 / 3} + b^{2 / 3} > 0

x^{2} - \frac{2}{3} x y + y^{2} > 0 true for x, y \in R ∖ {0}

Commented by Ndala last updated on 21/Dec/20

Thanks!

Facebook Tweet Pin