Question

If x^2 + 1\x^2=1 , then the value of x^3 +1\x^3 is
A. 3
B. 1
C √3
D 0​

Answer 1

Answer :

    " Option D → 0 " is correct

If x² + 1/x² = 1, then the value of x³ + 1/x³ is 0.

Solution :

Given, x² + 1/x² = 1

→ (x + 1/x)² - (2 * x * 1/x) = 1

→ (x + 1/x)² - 2 = 1

→ (x + 1/x)² = 1 + 2 = 3

→ x + 1/x = ± √3

Now, x³ + 1/x³

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

= (± √3)³ - 3(± √3)

= ± 3√3 - (± 3√3)

= 0

    Therefore, "option D" is correct.