2025 · Q13
If x^4 = x^2 + 1, where x > 0, then what is the value of 2x^4?
Elementary MathematicsAlgebra
- A2+√3
- B3+√5
- C5-2√3
- D3-√5
Explanation
x^4=x^2+1 is quadratic in x^2: x^2=(1+sqrt(5))/2 (positive root, x>0). Then 2x^4=2(x^2+1)=2(((1+sqrt(5))/2)+1)=3+sqrt(5). Substituting x^2+1 for x^4 directly is the shortcut; solving for x first is unnecessary.