The length of the line segment joining the two intersection points of the curves $$y = 4970 - |x|$$ and $$y = x^{2}$$ is_________.

If x>0:

$$y = 4970 - x$$ and $$y = x^{2}$$

Using these two equations, we get $$x^2+x=4970$$

The factors of 4970 is 71 and 70.

So, $$x^2+71x-70x-4970=0$$

$$x(x+71)-70(x+71)=0$$

x = -71 or 70

because x is positive x is 70

If x<0:

$$y = 4970 + x$$ and $$y = x^{2}$$

Using these two equations, we get $$x^2-x=4970$$

The factors of 4970 are 71 and 70.

So, $$x^2-71x+70x-4970=0$$

$$x(x-71)+70(x-71)=0$$

x = 71 or -70

Because x is negative, the possible value is x = -70

We are asked about the distance between the lines. It will be 70+70 = 140