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CTET Paper II (Mathematics and Science) 10 Jan 2023 Solved Paper

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Question : 36 of 150

Marks: +1, -0

x+\frac{1}{x}=4

, then the value of

x^{4}+\frac{1}{x^{4}}

is:

194
198
322
326

Solution:

Concept:

If

x + \frac{1}{x} = a

, then we can find higher powers using

x^2 + \frac{1}{x^2} = a^2 - 2

and

x^4 + \frac{1}{x^4} = \left(x^2 + \frac{1}{x^2}\right)^2 - 2

.

Explanation:

Given

x + \frac{1}{x} = 4

. First compute

x^2 + \frac{1}{x^2}

: square the given sum and subtract 2. So

4^2 - 2 = 16 - 2 = 14

.

Next, using this result, compute

x^4 + \frac{1}{x^4}

: square the value of

x^2 + \frac{1}{x^2}

and subtract 2. Thus

14^2 - 2 = 196 - 2 = 194

.

Answer:

A. 194

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