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Question Number 110727 by Study last updated on 30/Aug/20

a^2 +b^2 =10 , ab=13 , a^3 +b^3 =?

a2+b2=10,ab=13,a3+b3=?

Answered by mr W last updated on 30/Aug/20

(a+b)^2 =a^2 +b^2 +2ab=10+2×13=36 ⇒a+b=±6 (a+b)^3 =a^3 +b^3 +3ab(a+b) a^3 +b^3 =(a+b)^3 −3ab(a+b) =(a+b)(a^2 +b^2 −ab) =(±6)(10−13)=∓18

(a+b)2=a2+b2+2ab=10+2×13=36⇒a+b=±6(a+b)3=a3+b3+3ab(a+b)a3+b3=(a+b)3−3ab(a+b)=(a+b)(a2+b2−ab)=(±6)(10−13)=∓18

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