Question

if x^2+1/x^2 =7 then find the value of x^3+1/x^3

Answer 1

x^2+1/x^2 =7
=> x^2+1/x^2 +2 * x * 1/x -2 =7
=> (x + 1/x)^2  = 9
=> x + 1/x = 3 or -3

Now,

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

Now,Case - 1:-
x^3 + 1/x^3 = (3)^3 - 3(3) = 18

Case - 2:-
x^3 + 1/x^3 = (-3)^3 - 3(-3) = -18 

Answer 2

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