If a = 5 + √6 and b = 5 − √6, what is the value of a² + b²?
Show answer & explanation
Correct answer: C
Explanation
Given:
a = 5 + √6, b = 5 − √6
According to the formula:
a² + b² = (a + b)² − 2ab
a + b = 10
ab = (5 + √6)(5 − √6) = 25 − 6 = 19
a² + b² = 10² − 2×19
= 100 − 38
= 62