Verified answer

2x - sqrt{x^2+1} = 0

2x = sqrt{x^2+1}

4x^2 = x^2 + 1

3x^2 = 1

x = +-1/sqrt(3)

If x = -1/sqrt(3)

then -2/sqrt(3) = sqrt(1/sqrt(3)^2 + 1) = sqrt(1/3+1) sqrt(4/3) = 2/sqrt(3)

and the two sides are different so x=-1/sqrt(3) is extraneous

sol is x = 1/sqrt(3) = sqrt(3)/3

The intersection with the x-axis means y = 0

Hence

0 = 2x -/+ sqrt(x^2 + 1)

2x = +- sqrt(x^2 -+1)

Square up both sides, this will remove the 'square root'.

4x^2 = x^2 + 1

3x^2 = 1

x^2 = 1/3

x = +/- sqrt(1/3) or +/- sqrt(0.333...)

y=2x-\sqrt{x^2+1} ....y must = 0 on the x-axis

why is the slash in the problem??

0 = 2x - sqrt{x^2+1}

2x = sqrt{x^2+1} <<< square both sides

4x^2 = x^2 - 1

3x^2 = -1

x^2 = -1/3

x = +/- sqrt {-1/3} <<< imaginary answers, not real

so this does NOT intersect the x-axis