Question

If 4x² – 7x + 1 = 0, find x² + 1/16x²

1. 34/6
2. 41/16
3. 33/4
4. 45/8

Answer 1

Correct Answer - Option 2 : 41/16

Given:

4x² – 7x + 1 = 0

Formula used:

(a + b)² = a² + b² + 2ab

Calculation:

According to the question,

⇒ 4x² – 7x + 1 = 0

⇒ x(4x – 7 + 1/x) = 0

⇒ 4x – 7 + 1/x = 0

⇒ 4x + 1/x = 7

Multiply both the sides with ¼

⇒ 1/4(4x + 1/x) = 7/4

⇒ x + 1/4x = 7/4

Squaring both sides,

⇒ (x + 1/4x)² = (7/4)²

⇒ x² + 1/16x² + 2(x)(1/4x) = 49/16

⇒ x² + 1/16x² + 1/2 = 49/16

⇒ x² + 1/16x² = 49/16 – 1/2

⇒ x² + 1/16x² = (49 – 8)/16

⇒ x² + 1/16x² = 41/16

∴ The value of x² + 1/16x² is 41/16.