If 4x⁴ = 5x²- 1, x > 1/(sqrt2) , then what is the value of (2x² - x - 1)?

If 4x⁴ = 5x²- 1, x > 1/(sqrt2) , then what is the value of…

If 4x⁴ = 5x²- 1, x > $\frac{1}{\sqrt2}$ , then what is the value of (2x² - x - 1)?

Show answer & explanation

Correct answer: C

Explanation

The correct answer is Option 3. i.e 0.

⇒ 4x⁴ = 5x²- 1

⇒ 4x⁴ - 5x²+ 1 = 0

⇒ 4x⁴ - 4x² - x² + 1 = 0

⇒ 4x² (x² - 1) -1( x² - 1)= 0

⇒ (x² - 1) ( 4x² - 1) = 0.

⇒ x = 1 and 1/2 (i.e. 1/2 is not possible because x > $\frac{1}{\sqrt2}$ ).

⇒ x = 1.

⇒ (2x² - x - 1) = 2 × 1 - 1 + 1 = 0