Correct Option: A

Given in the question ,
x - 1 = √2 + √3
On squaring both sides ,
x ² – 2x + 1 = 2 + 3 + 2√6
⇒ x ² - 2x - 4 = 2 √6
On squaring again,
⇒ x⁴ + 4x² + 16 – 4x³ – 8x² + 16x = 24
⇒ x⁴ – 4x³ – 4x² + 16x – 8 = 0
⇒ 2x⁴ – 8x³ – 8x² + 32x – 16 = 0
⇒ 2x⁴ – 8x³ – 5x² + 26x – 28 – 3x² + 6x + 12 = 0
⇒ 2x⁴ – 8x³ – 5x² + 26x – 28 = 3x² – 6x – 12
⇒ 2x⁴ – 8x³ – 5x² + 26x – 28 = 3 (x² – 2x – 4)
⇒ 2x⁴ – 8x³ – 5x² + 26x – 28 = 3 x 2√6 = 6 √6