Discussion

Explanation:

x + 1 = x²
⇒ x² - x – 1 = 0
⇒ x = (1+√5)/2 (∵ x > 0)

Now, squaring the original equation, we get

(x  +1)² = x⁴
⇒ x² + 1 + 2x = x⁴
⇒ x⁴ = x + 1 + 1 + 2x (Since, x² = x + 1)
⇒ x⁴ = 3x + 2
⇒ 2x⁴ = 6x + 4
⇒ 2x⁴ = 6((1+√5)/2) + 4
​​​​​​​⇒ 2x⁴ = 7 + 3√5

Alternately,
We know, x = (1+√5)/2
⇒ x ≈ 1.62
∴ 2x⁴ ≈ 13.8

option I ≈ 14.8,
option II ≈ 11.6,
option IV ≈13.6

Hence, option (d).

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