If x^2 - 3x + 1 = 0 where ( x ≠ 0 ) then the value of x^3 - 1/ x^3 is = ?

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Solution

x² - 3x +1 =0 (given)

On dividing LHS & RHS of the above equation by x

We get, x - 3 +1/x =0

=> x+1/x =3…………..(1)

So, the value of
x²+2.(x)(1/x)+1/x² =9

(x² + 1/x²)=7

(x- 1/x)^2 = (x^2 + 1/x^2)-2
=7-2=5

so (x- 1÷x)=√5

x^3 - 1/x^3
= (x- 1/x)(x^2+1+ 1/x^2)
= √5 × (7+1)
=8√5

Like if satisfied

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