alleryFind (x − 1/x)² if x + 1/x = 4:
A8
B10
C12
D14
Answer & Solution
Correct answer: C. 12
(x + 1/x)² = x² + 2 + 1/x², so x² + 1/x² = 4² − 2 = 14. Then (x − 1/x)² = x² − 2 + 1/x² = 14 − 2 = 12. (Beautiful: two identities together.)
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