What is the answer to sqrt(x-\sqrt{1-x)+sqrt(x)}=1 ?

The answer to sqrt(x-\sqrt{1-x)+sqrt(x)}=1 is x\approx 0.70440…

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

x - 1 - x + x = 1

x \approx 0.70440 \dots

Solution steps

x - 1 - x + x = 1

Remove square roots

- 4 x^{3} + 12 x^{2} - 12 x + 4 = x^{4} - 8 x^{3} + 20 x^{2} - 16 x + 4

Switch sides

x^{2} - 2 1 - x x - 3 x + 2 1 - x + 2 = x

Move

x^{2}

to the right side

- 2 1 - x x - 3 x + 2 1 - x + 2 = x - x^{2}

Move

3 x

to the right side

- 2 1 - x x + 2 1 - x + 2 = - x^{2} + 4 x

Move

2

to the right side

- 2 1 - x x + 2 1 - x = - x^{2} + 4 x - 2

Factor

- 2 1 - x x + 2 1 - x : 2 1 - x (- x + 1)

2 1 - x (- x + 1) = - x^{2} + 4 x - 2

Solve

- 4 x^{3} + 12 x^{2} - 12 x + 4 = x^{4} - 8 x^{3} + 20 x^{2} - 16 x + 4 : x = 0, x \approx 0.70440 \dots

x = 0, x \approx 0.70440 \dots

Verify Solutions:

x = 0

False

, x \approx 0.70440 \dots

True

The solution is

x \approx 0.70440 \dots

x - 21 - 4 x = 0

m = - 3, 3 x^{2} - 15 x + 2 m = 0

x = 34

(x^{2} + 72)^{\frac{1}{2}} = 9

x + 1 - x - 6 = 1

What is the answer to sqrt(x-\sqrt{1-x)+sqrt(x)}=1 ?
The answer to sqrt(x-\sqrt{1-x)+sqrt(x)}=1 is x\approx 0.70440…
Solve for x: sqrt(x-\sqrt{1-x)+sqrt(x)}=1
The solution is x\approx 0.70440…