If a = √7 + √5 and b = √7 - √5, then a² + b² = ?
Show answer & explanation
Correct answer: C
Explanation
Given:
a = √7 + √5
b = √7 − √5
By the formula:
(a + b)² = a² + b² + 2ab
a² = (√7 + √5)²
= 7 + 5 + 2√35
= 12 + 2√35
b² = (√7 − √5)²
= 7 + 5 − 2√35
= 12 − 2√35
a² + b² = (12 + 2√35) + (12 − 2√35) = 24