Question

The number of real roots of (6 – x)⁴ + (8 – x)⁴ = 16 is –

• A. 0
• B. 2
• C. 5
• D. 4

Answer 1

Answer: (B)

2

Answer 2

Let y = $\frac{6 - x + 8 - x}{2}$⇒ x = 7 – y

∴ (y – 1)⁴ + (y + 1)⁴ = 16

⇒ y⁴ + 6y² – 7 = 0

⇒ y² = 1 ⇒ y = ± 1

⇒ 7 – x = ± 1 ⇒ x = 6, 8