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Question Number 27112 by NECx last updated on 02/Jan/18

Commented by NECx last updated on 02/Jan/18

$p l e a s e h e l p w i t h t h e b o t h . . . T h a n k s$
Commented by prakash jain last updated on 05/Jan/18
$(x+y)^3 =x^3 +y^3 +3xy(x+y) x^3 +y^3 −x^2 y−xy^2 =(x+y)^3 −4xy(x+y) =(x+y){(x+y)^2 −4xy} =(x+y)(x−y)^2 ≥0 ∵ (x+y)>0 and (x−y)^2 ≥0 The inequality is question 14 should be ≥ for the case x=y.$
${(x + y)}^{3} = x^{3} + y^{3} + 3 x y (x + y)$ $x^{3} + y^{3} - x^{2} y - {x y}^{2}$ $= {(x + y)}^{3} - 4 x y (x + y)$ $= (x + y) {{(x + y)}^{2} - 4 x y}$ $= (x + y) {(x - y)}^{2} ⩾ 0$ $∵ (x + y) > 0 and {(x - y)}^{2} ⩾ 0$ $The inequality is question 14$ $should be ⩾ for the case x = y .$
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