Question: If \(x^2+\frac{1}{x^2}=4\), what is the value of \(x^4+\frac{1}{x^4}\)?

1. 10
2. 12
3. 14
4. 16
5. 18

Correct Answer: (C)
Solution and Explanation:
Approach Solution 1:

The problem statement states that

Given:

• x^2 + 1/x^2 = 4

Find out:

• The value of x^4 + 1/x^4

By squaring the equation x^2 + 1/x^2 = 4, we get:
=> x^4 + 2∗ x^2∗ 1/x^2 +1/x^4 =16
=> x^4 + 2 + 1/x^4 =16
=> x^4 + 1/x^4 =14

Therefore, the value of x^4 + 1/(x^4) = 14

Approach Solution 2:

The problem statement informs that

Given:

• x^2 + 1/x^2 = 4

Find out:

• The value of x^4 + 1/x^4

Hence, x^4 + (1/x^4) can be written as
= (x^2)^2 + (1/x^2)^2
= (x^2 + 1/x^2)^2 - 2x^2(1/x^2)
=4^2-2 = 14.

Therefore, the value of x^4 + 1/(x^4) = 14

Approach Solution 3:

The problem statement discloses that

Given:

• x^2 + 1/x^2 = 4

Find out:

• The value of x^4 + 1/x^4

Let x^2 + 1/x^2 = k,
Then x^4 + 1/x^4 = k^2 - 2
As stated in the question, x^2 + 1/x^2 = 4,
Then x^4 + 1/x^4 = (4)^2 - 2 = 14
Therefore, the value of x^4 + 1/(x^4) = 14

“If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4''- asks the candidates to use their abilities to solve the problem. It is a topic of the GMAT Quantitative reasoning section of the GMAT exam. It has been taken from the book “GMAT Official Guide Quantitative Review 2021”. GMAT Problem Solving questions are created with the intention of testing candidates’ numerical literacy to solve quantitative problems. GMAT Quant practice papers enable the candidates to practice several questions that will help them to improve their calculative skills.

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