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The length of the line segment joining the two intersection points of the curves $$y = 4970 - |x|$$ and $$y = x^{2}$$ is_________.
Correct Answer: 140
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
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