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If x^2+1/x^2=7, find the value of x^3+1/x^3

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If x2+1x2=7,find the value of x3+1/x3,taking only the positive value of x+1/x

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Given Equation is x^2 + 1/x^2 = 7

We know that (x + 1/x)^2 = x^2 + 1/x^2 + 2 * x * 1/x

= x^2 + 1/x^2 + 2

= 7 + 2

= 9

(x + 1/x) = 3

Now,

(x^3 + 1/x^3) = (x + 1/x)^3 - 3 * x * 1/x * (x + 1/x)

= (x + 1/x)^3 - 3(x + 1/x)

= (3)^3 - 3(3)

= 27 - 9

= 18.

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