Question 1206802

Solve for{{{ x}}},


{{{sqrt(x) + sqrt(x - sqrt(1-x)) = 1}}}

{{{ sqrt(x - sqrt(1-x)) = 1-sqrt(x) }}}...square both sides

{{{(sqrt(x - sqrt(1-x)))^2 =( 1-sqrt(x))^2 }}}

{{{x - sqrt(1-x) = 1-2sqrt(x)+x}}}...simplify

{{{- sqrt(1-x) = 1-2sqrt(x)}}}...square both sides

 {{{(- sqrt(1-x))^2 = (1-2sqrt(x))^2}}}

{{{1-x =1 - 4sqrt(x) +4x}}}

{{{4sqrt(x)=1 - 1 +4x+x}}}

{{{4sqrt(x)=5x}}}...square both sides

{{{16x=25x^2}}}..simplify

{{{16=25x}}}

{{{x=16/25}}}