If x²- 7x + 1 = 0, and 0 < x < 1, what is the value of x²- \(\frac{1}{x^2}\) ?

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 19 Jul 2023 Shift 3)

Answer 1

Formula Used :

x + (1/x) = a

Then x - (1/x) = √(a² - 4)

Calculation :

⇒ x² - 7x + 1 = 0

On dividing by x we get :

⇒ x - 7 + (1/x) = 0

⇒ x + (1/x) = 7

Now, (x - 1/x) = -√(49 - 4) = - √45 = - 3√5

[Here 0 < x < 1 so x - (1/x) < 0]

⇒ x² - (1/x²) = [x - (1/x)] [x + (1/x)]

⇒ 7 × (-3√5)

⇒ -21√5

∴ The correct answer is - 21√5.

Mistake Points

Here 0 < x < 1

⇒ 1/x > 1

⇒ x - 1/x < 0

Thus, x² - (1/x²) = [x - (1/x)] [x + (1/x)] < 0