If a = 3 + √2, b = 3 − √2, then what is the value of a² + b²?
Show answer & explanation
Correct answer: B
Explanation
Given:
a = 3 + √2, b = 3 − √2
According to the formula:
(a + b)² = a² + b² + 2ab
a + b = 6
ab = (3 + √2)(3 − √2) = 9 − 2 = 7
⇒ a² + b² = (a + b)² − 2ab
= 6² − 2×7
= 36 − 14
= 22