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**

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