If x = √3 + √2, then find the value of x² - 2√6.
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Correct answer: C
Explanation
Given:
x = √3 + √2
By the formula:
(a + b)² = a² + b² + 2ab
x² = (√3 + √2)²
= (√3)² + (√2)² + 2 × √3 × √2
= 3 + 2 + 2√6
= 5 + 2√6
x² − 2√6 = (5 + 2√6) − 2√6 = 5