Question 651887

{{{ sqrt(x)-sqrt(x-20)=10}}}
if the answer is {{{36}}}, than {{{ sqrt(36)-sqrt(36-20)=10}}}...->..{{{ 6-sqrt(16)=10}}}.->..{{{ 6-4=10}}}->..{{{ 2=10}}},,,which is not true

you probably made mistake using minus sign

with plus sign you will get:

{{{sqrt(x)+sqrt(x-20)=10}}}

{{{(sqrt(x)+sqrt(x-20))^2=10^2}}}

{{{sqrt(x)^2+2sqrt(x)sqrt(x-20)+sqrt(x-20)^2=100}}}

{{{x+2sqrt(x)sqrt(x-20)+(x-20)=100}}}

{{{2x+2sqrt(x(x-20))-20=100}}}

{{{2x+2sqrt(x(x-20))=100+20}}}

{{{2sqrt(x(x-20))=-2x+120}}}

{{{(2sqrt(x(x-20)))^2=(-2x+120)^2}}}

{{{4(x(x-20))=(-2x)^2-2(2x)*120+120^2}}}

{{{4(x^2-20x)=4x^2-480x+14400}}}

{{{4x^2-80x=4x^2-480x+14400}}}

{{{cross(4x^2)-80x=cross(4x^2)-480x+14400}}}

{{{-80x=-480x+14400}}}

{{{-80x+480x=14400}}}

{{{400x=14400}}}

{{{x=14400/400}}}

{{{x=36}}}