GATE 2016 CS (CS2) – Question 5

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

In a quadratic function, roots α and β satisfy αβ = 4. Find $(\alpha^n+\beta^n)/(\alpha^{-n}+\beta^{-n})$.

$n^4$
$4^n$
$2^{2n-1}$
$4^{n-1}$

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Correct answer: (B) $4^n$

Explanation

Rewrite the denominator as $(\alpha^n+\beta^n)/(\alpha\beta)^n$. Wherever the stated ratio is defined, cancellation gives $(\alpha\beta)^n=4^n$, B. The nonzero product ensures both negative powers exist.

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