If x is not equal to zero, and x + 1/x = 3, then what is the value of x^4 + 1/x_4? GMAT Problem Solving

Question: If x is not equal to zero, and \(x+\frac{1}{x}=3\), then what is the value of \(x^4+ (\frac{1}{x^4})\)?

1. 27
2. 32
3. 47
4. 64
5. 81

‘If x is not equal to zero, and \(x+\frac{1}{x}=3\), then what is the value of \(x^4+ (\frac{1}{x^4})\)?’ - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation

Approach Solution 1:

There is only one way to solve this problem.

This is a simple simplification sum. This has to be solved using the (a + b)² formula.

Given,

\(x+\frac{1}{x}=3\)

squaring both the sides, we get,

\(x^2+\frac{1}{x^2}=7\)

again squaring both the sides, we get,

Now, (\(x^2+\frac{1}{x^2}\))² =\(x^4+\frac{1}{x^4}+2\)

that implies, \(7^2=x^4+\frac{1}{x^4}+2\)

that implies, \(49=x^4+\frac{1}{x^4}+2\)

that implies, \(x^4+\frac{1}{x^4}\) = 49 - 2 = 47

Therefore, the required answer is 47. Hence option C is the correct answer.

Correct Answer: C

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