Question 86210
a) x-2sqrt(x) = 0

==> sqrt(x) [sqrt(x) - 2] = 0 [taking sqrt(x) common]

==> sqrt(x) = 0 or sqrt(x) - 2 = 0

==> x = 0 or sqrt(x) = 2

==> x = 0 or x = 4 (on squaring)

So the solution is x = 0 or x = 4



b) The following graph shows the equations drawn on the same axes.

{{{ graph( 300, 200, -6, 5, -10, 10, x, 2sqrt(x)) }}}

The red line shows y = x and the green curve shows y = 2 sqrt(x)

From the graph also we infer that the equations intersect at x = 0 and x = 4.

Thus the points of intersection are (0,0) and (4,4)