Question

If x^2+1/x^2=1then the value of x^3+1/x^3is

Answer 1

Answer:

x³+1/x³ = 0

It is given that,

x²+1/x² = 1 ---(1)

=> x² + 1/x² +2 = 1 + 2

=> ( x + 1/x )² = 3

=> (x+1/x ) = ± √3 ----(2)

Now ,

x³+1/x³

= (x+1/x)³ -3(x+1/x)

Case - 1

If x +1/x = √3

then

x³+1/x³ = (√3)³ -3×√3

= 3√3-3√3

= 0

Case - 2

if x+1/x = -√3

then

x³+1/x³

= (-√3)³ - 3(-√3)

= -3√3 + 3√3

= 0

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