On Apr 6, 9:09 am, Danread5 <danre...@me.com> wrote: > > sage: d = sqrt(x^2 + 5^2) > sage: D = sqrt((20-x)^2 + 10^2) > sage: T = d + D; T > sqrt(x^2 + 25) + sqrt((x - 20)^2 + 100) > sage: diff(T, x) > (x - 20)/sqrt((x - 20)^2 + 100) + x/sqrt(x^2 + 25) > sage: solve((x - 20)/sqrt((x - 20)^2 + 100) + x/sqrt(x^2 + 25) == 0, > x) > [x == 20*sqrt(x^2 + 25)/(sqrt(x^2 + 25) + sqrt(x^2 - 40*x + 500))] > > For some reason, Sage isn't solving completely for x, or isn't > 'seeing' the x^2... > > Any help gladly appreciated!
This problem can be easily solved mentally - "Find the point on the x-axis, the sum of distances of which to (0, 5) and (20, -10) is minimal." Of course, it is the point of intersection of the line connecting these points and the x-axis. Now, it is obvious from the picture including also vertical lines at x=0 and x =20, that the 2 triangles are similar. The left triangle has height 5, and the right one has hight 10, twice greater, so their sides on the x-axis also have the same ratio, 1:2, i.e. the length of the horizontal side of the left triangle is 1/3 of the distance from 0 to 20, i.e. 20/3. Alec -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
