If x = 1 + 2 + 3 then find the...

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If x = 1 + √2 + √3, then find the value of x² - 2x + 4.

A. 2(7 + √6)

B. 2(4 + √6)

C. 2(3 + √7)

D. (4 + √6)

Answer: Option B

Solution(By Examveda Team)

x = 1 + √2 + √3
⇒ x - 1 = √2 + √3
On squaring both sides,
(x - 1)² = (√2 + √3)²
⇒ x² - 2x + 1 = 2 + 3 + 2√6
Add 3 both side
⇒ x² - 2x + 4 = 5 + 2√6 + 3
⇒ x² - 2x + 4 = 8 + 2√6
⇒ x² - 2x + 4 = 2(4 + √6)

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