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Given-that-x-y-2-x-2-y-2-6-find-the-value-of-x-3-y-3-

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Question Number 131333 by ZiYangLee last updated on 03/Feb/21
Given that { ((x+y=2)),((x^2 +y^2 =6)) :} find the value of x^3 +y^3 .
Giventhat{x+y=2x2+y2=6findthevalueofx3+y3.
Answered by mr W last updated on 03/Feb/21
x^2 +y^2 =(x+y)^2 −2xy 6=2^2 −2xy ⇒xy=−1 x^3 +y^3 =(x+y)^3 −3xy(x+y) =2^3 −3(−1)(2) =14
x2+y2=(x+y)2−2xy6=22−2xy⇒xy=−1x3+y3=(x+y)3−3xy(x+y)=23−3(−1)(2)=14

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