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In a quadratic function, the value of the product of the roots (α, β) is 4. Find the value of
(αⁿ + βⁿ)/(α^−n + β^−n)
- n⁴
- 4ⁿ
- 2^(2n-1)
- 4^(n-1)
Correct answer: 4ⁿ
Solution
Since a^-n + b^-n = (b^n + a^n)/(ab)^n, the ratio (a^n+b^n)/(a^-n+b^-n) equals (ab)^n. With ab=4 this is 4^n, which is index 1, not the stored 4^(n-1).
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