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GATE 2016 EE – Question 5

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

In a quadratic function, the value of the product of the roots $(\alpha, \beta)$ is 4. Find the value of

$$\frac{\alpha^n + \beta^n}{\alpha^{-n} + \beta^{-n}}$$

  1. $n^4$
  2. $4^n$
  3. $2^{2n-1}$
  4. $4^{n-1}$

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Correct answer: (B) $4^n$

Explanation

Write $\alpha^{-n} + \beta^{-n} = \frac{\beta^n + \alpha^n}{(\alpha\beta)^n}$. Dividing the numerator $\alpha^n + \beta^n$ by this gives $(\alpha\beta)^n = 4^n$.