If a = 6 + √5 and b = 6 − √5, what is the value of a² + b²?
Show answer & explanation
Correct answer: A
Explanation
Given:
a = 6 + √5, b = 6 − √5
According to the formula:
a² + b² = (a + b)² − 2ab
a + b = (6 + √5) + (6 − √5) = 12
ab = (6 + √5)(6 − √5) = 36 − 5 = 31
a² + b² = 12² − 2 × 31
= 144 − 62
= 82