cubic identity

Algebra Level 3

If x 3 − y 3 = 4 \sqrt[3]{x}-\sqrt[3]{y}=4 and x − y = 4 x-y=4 , find x × y x\times y


The answer is -125.

Barack Clinton by Barack Clinton , 32, Switzerland

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1 solution

Barack Clinton
Feb 14, 2015

Let x 3 = A , x 3 = B \sqrt[3]{x}=A, \sqrt[3]{x}=B then; A 3 = x , B 3 = y A^3=x, B^3=y and A − B = 4 A-B=4 A 3 − B 3 = ( A − B ) 3 + 3 A B ( A − B ) A^3-B^3=(A-B)^3+3AB(A-B) 4 = 4 3 + 3 × x y 3 × 4 4=4^3+3\times \sqrt[3]{xy}\times 4 4 = 64 + 12 × x y 3 4=64+12\times\sqrt[3]{xy} ⇒ x y 3 = − 5 \Rightarrow\sqrt[3]{xy}=-5 and x y = − 125 xy=-125

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