if a+b=10 and ab =21 ,find the value of a^3+b^3 .

Answers (1)

solution: we know that 

                 (a^3+b^3) =(a+b)(a^2-ab+b^2)

                    Rightarrow a^3+b^3=(a+b)(a^2+2ab+b^2-2ab-ab)  [adding and subtraqcting 2ab in the second bracket]

                   Rightarrow a^3+b^3=(a+b) left  (a+b)^2 -3ab
ight

                  Rightarrow a^3+b^3=10	imes(10^2-3	imes21)=10	imes(100-63)=10	imes37=370

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