A) 96
B) 14
C) \[96\sqrt{2}\]
D) \[14\sqrt{2}\]
Correct Answer: D
Solution :
\[f(x)=\sqrt{{{(2x+7)}^{2}}+{{6}^{2}}}+\sqrt{{{(2x-7)}^{2}}+{{8}^{2}}}\] |
This is sum of distance of \[P=(2x,\,\,7)\]from \[A=(-7,\,\,1)\]and \[B=(7,15)\] |
By triangle inequality the minimum occurs when P, A, B are collinear with P lying between A and B. |
\[\therefore \,\,\,\,AB=\sqrt{{{14}^{2}}+{{14}^{2}}}=14\sqrt{2}\] |
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