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x-y-x-2-xy-y-2-2-x-3-y-3-x-9-y-9-8-

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Question Number 190942 by mathlove last updated on 14/Apr/23
(x+y)(x^2 −xy+y^2 )=2 ((x^3 y^3 )/(x^9 +y^9 −8))=?
(x+y)(x2−xy+y2)=2x3y3x9+y9−8=?
Answered by Frix last updated on 15/Apr/23
x^3 +y^3 =2 ⇒ y^3 =2−x^3 ((x^3 (2−x^3 ))/(x^9 +(2−x^3 )^3 −8))=((x^3 (2−x^3 ))/(−6x^3 (2−x^3 )))=−(1/6)
x3+y3=2⇒y3=2−x3x3(2−x3)x9+(2−x3)3−8=x3(2−x3)−6x3(2−x3)=−16
Answered by manxsol last updated on 15/Apr/23
x^3 +y^3 =2 (x^3 +y^3 )^3 =x^9 +y^9 +3x^3 y^3 (x^3 +y^3 ) 8=x^9 +y^9 +6x^3 y^3 −6x^3 y^3 =x^9 +y^9 −8 ((x^3 y^3 )/(−6x^3 y^3 ))=−(1/6)
x3+y3=2(x3+y3)3=x9+y9+3x3y3(x3+y3)8=x9+y9+6x3y3−6x3y3=x9+y9−8x3y3−6x3y3=−16

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