We have to solve the equation sqrt (x + sqrt (1 - x)) + sqrt x = 1
sqrt (x + sqrt (1 - x)) + sqrt x = 1
sqrt (x + sqrt (1 - x)) = 1 - sqrt x
square both the sides
=> x + sqrt(1...
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We have to solve the equation sqrt (x + sqrt (1 - x)) + sqrt x = 1
sqrt (x + sqrt (1 - x)) + sqrt x = 1
sqrt (x + sqrt (1 - x)) = 1 - sqrt x
square both the sides
=> x + sqrt(1 - x) = 1 + x - 2 sqrt x
=> sqrt(1 - x) = 1 - 2 sqrt x
square both the sides
=> 1 - x = 1 + 4x - 4 sqrt x
=> 5x = 4 sqrt x
square both the sides
25x^2 = 16x
=> 25x^2 - 16x = 0
=> x(25x - 16) = 0
=> x = 0 and x = 16/25
The required values of x are 0 and 16/25