If a = 7 + √2, b = 7 − √2 then what is the value of a² + b²?
Show answer & explanation
Correct answer: C
Explanation
Given:
a = 7 + √2, b = 7 − √2
According to the formula:
a² + b² = (a + b)² − 2ab
a + b = 14
ab = (7 + √2)(7 − √2) = 49 − 2 = 47
a² + b² = 14² − 2×47
= 196 − 94
= 102