if x^2+1/x^2 =7 , find the value of x^3 +1/x^3 .?

Answers (1)

solution:  we have ,

            (x+frac1x)^2= x^2 +frac1x^2+2	imes x	imesfrac1x

   Rightarrow (x+frac1x)^2=x^2+frac1x^2+2

 Rightarrow (x+frac1x)^2=7+2    putting x^2+frac1x^2=7

Rightarrow (x+frac1x)^2=9

Rightarrow (x+frac1x)^2=3^2

Rightarrow x+frac1x=3

Rightarrow(x+frac1x)^3=3^3           [cubing both sides ]

Rightarrow x^3+frac1x^3+3(x+frac1x)= 27

Rightarrow (x^3+frac1x^3)+3	imes3=27Rightarrow x^3+frac1x^3=27-9Rightarrow x^3+frac1x^3=18

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