The length of the line segment joining the two intersection points of the curves y = 4970 - lxl and y = x2 is
Explanation:
y = 4970 - |x| & y = x2
To find intersection point we equate both equations. ⇒ 4970 - |x| = x2 ⇒ x2 + |x| - 4970 = 0 ⇒ |x|2 + |x| - 4970 = 0 [x2 = |x|2] ⇒ |x|2 + 71|x| - 70|x| - 4970 = 0 ⇒ (|x| + 71)(|x| - 70) = 0 ⇒ |x| = - 71 or 70 [- 71 rejeceted as |x| cannot be negative]
⇒ x = + 70 or - 70
∴ Line joining the intersection point of these graphs will be a horizontal line. The x coordinates of its end points are +70 & -70. ∴ Distance between the two points = 70 + 70 = 140.
Hence, 140.
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