1. If $$x^3 - y^3 = 81$$ and $$x - y = 3$$, then what is the value of $$x^2 + y^2$$ ?
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By: anil on 05 May 2019 01.46 am
Given : $$x^3 - y^3 = 81$$ ---------------(i) and $$x - y = 3$$ -----------(ii) Cubing both sides, => $$(x-y)^3=(3)^3$$ => $$x^3-y^3-3xy(x-y)=27$$ Substituting values from equations (i) and (ii), we get : => $$81-3xy(3)=27$$ => $$9xy=81-27=54$$ => $$xy=frac{54}{9}=6$$ ------------(iii) Also, $$(x-y)^2=x^2+y^2-2xy$$ Substituting values from equations (ii) and (iii), we get : => $$(3)^2=(x^2+y^2)-2(6)$$ => $$9=(x^2+y^2)-12$$ => $$x^2+y^2=9+12=21$$ => Ans - (B)
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