if a+b =10 and a^2+b^2 =58 , find the value of a^3+b^3 .

Answers (1)

solution: we know that left ( a+b 
ight )^2 = a^2 + b^2 + 2ab

                putting      a+b=10  and a^2+b^2=58, we gate

              10^2=58+2abRightarrow 100=58+2abRightarrow 100-58=2abRightarrow 42=2abRightarrow ab=21

    thus ,we have 

                           a+b=10 and ab=21

   now, 

                          left ( a+b 
ight )^3=a^3+b^3+3ab(a+b)

                              Rightarrow 10^3=a^3+b^3+3	imes 21	imes 10

                            Rightarrow 1000=a^3+b^3+630

                         Rightarrow 1000-630=a^3+b^3Rightarrow 370=a^3+b^3

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