On Coordinate Geometry and the Triangular Inequality.

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We have three Points P(2,3),Q(4,-2) and R(x,0).We need to find the value of x such that: The Triangle

Case1 : PR+RQ is maximum. x=16/5

Case 2 : PR-RQ is minimum. x=8

I absolutely have no idea how to solve this.We need to solve x for both the cases.