What is the multiplicative inverse of (√2 + 1)^20?
A.v
B.v² − 1
C.v²✓ Correct
D.v² + 1
Explanation
Since (√2 + 1)(√2 − 1) = 2 − 1 = 1, we have (√2 − 1) = 1/(√2 + 1). Therefore (√2 − 1)^20 = 1/(√2 + 1)^20, which is the multiplicative inverse of (√2 + 1)^20. Given v = (√2 − 1)^10, so (√2 − 1)^20 = v². Hence the multiplicative inverse is v².
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