if a-b =4 and ab=45 ,find the value of a^3-b^3 .

Answers (1)

solution : we have ,

               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 subtracting 2ab in the second bracket]

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

         Rightarrow a^3-b^3=4	imes(4^2+3	imes45)=4	imes(16+135)=4	imes151=604

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