2025 · Q26
If x - 1/x = 2, where x > 0, then what is the value of x^2 - 1/x^2?
Elementary MathematicsAlgebra
- A2√2
- B4√2
- C6√2
- D8√2
Explanation
x^2-1/x^2=(x-1/x)(x+1/x)=2(x+1/x). From (x+1/x)^2=(x-1/x)^2+4=8 and x>0, x+1/x=2*sqrt(2). Hence x^2-1/x^2=4*sqrt(2). The sign of x+1/x (positive) is fixed by x>0.