Correct Option: D

x = 1 + √2 + √3
⇒ x - 1 = √3 + √2
On squaring both sides ,
x² – 2x + 1 = 3 + 2 + 2√6
⇒ x² – 2x + 1 - 5 = 2√6
⇒ x² – 2x - 4 = 2√6
On squaring again,
(x² – 2x - 4)² = (2√6)²
⇒ x⁴ + 4x² + 16 – 4x³ + 16x - 8x² = 24
⇒ x⁴ – 4x³ - 4x² + 16x - 8x² - 8 = 0
⇒ 2x⁴ – 8x³ - 8x² + 32x - 16 = 0
∴ 2x⁴ – 8x³ - 5x² + 32x - 16 + 3x² - 6x - 12
= 0 + 3 (x² – 2x – 4) = 3 × 2√6
Required answer = 6√6