Question 1160834
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            I will present here another way to solve the problem.



<pre>
On the line (x,5x+1) we want to find the point closest to (3,5).


Write the distance formula (the square of distance formula)


    d^2 = (x-3)^2 + (5x+1-5)^2 = 

          (x-3)^2 + (5x-4)^2 = x^2 - 6x + 9 + 25x^2 - 40x + 16 = 

                             = 26x^2 - 46x + 25.


The minimum of this quadratic form is at  x = {{{-b/(2a)}}} = {{{46/(2*26)}}} = {{{23/26}}}.


<U>ANSWER</U>.  The closest point is  ( {{{23/26}}},{{{5*(24/26)+1}}} ) = ( {{{23/26}}},{{{141/26}}} ).
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Solved.