Question 985456


{{{x/2}}} - {{{sqrt(x)}}} = {{{24}}}, 


{{{x/2 - 24}}} = {{{sqrt(x)}}}, 


{{{(x/2 - 24)^2}}} = {{{(sqrt(x))^2}}} 


{{{(x/2)^2 - 2*(x/2)*24 + 24^2}}} = {{{x}}},


{{{x^2/4 - 24x - x + 24^2}}} = {{{0}}}, ---> (multiply both sides by {{{4}}} ) --->


{{{x^2 - 100x + 4*24^2}}} = {{{0}}},


{{{x^2 - 100x + 2304}}} = {{{0}}}.


{{{x[1]}}} = {{{(100+sqrt(100^2-4*2304))/2}}} = {{{(100+sqrt(784))/2}}} = {{{(100+28)/2}}} = {{{128/2}}} = 64,


{{{x[2]}}} = {{{(100-sqrt(100^2-4*2304))/2}}} = {{{(100-sqrt(784))/2}}} = {{{(100-28)/2}}} = {{{72/2}}} = 36.


<U>Check</U>. 1. &nbsp;{{{64/2 - sqrt(64)}}} = {{{32 - 8}}} = {{{24}}}. &nbsp;&nbsp;&nbsp;&nbsp;<B>Yes</B>!


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2. &nbsp;{{{36/2 - sqrt(36)}}} = {{{18 - 6}}} = {{{12}}}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<B>No</B>!


Only the root <B>64</B> satisfies the given condition.


<B>Answer</B>. &nbsp;My earning is &nbsp;<B>64</B>. &nbsp;&nbsp;(64 of what ? :)