Carcass wrote:
If \(x^2 + \frac{1}{x^2} = 4\), what is the value of \(x^4 + \frac{1}{x^4}\) ?
A. 10
B. 12
C. 14
D. 16
E. 18
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITIONGRE - Math BookIMPORTANT: I notice that if we SQUARE x², we get x⁴, and if we SQUARE 1/x², we get 1/x⁴, so let's see what happens if we take the equation x² + 1/x² = 4 and
SQUARE both sides:
(x² + 1/x²)
² = 4
²So, (x² + 1/x²)(x² + 1/x²) = 16
Expand to get: x⁴ + 1 + 1 + 1/x⁴ = 16
Simplify: x⁴ + 1/x⁴ = 14
Answer: C
Cheers,
Brent