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

The answer to sqrt(x)+sqrt(x+\sqrt{x)}=1 is x= 1/9

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

x + x + x = 1

x = \frac{1}{9}

Decimal Notation

x = 0.11111 \dots

Solution steps

x + x + x = 1

Remove square roots

x = \frac{1}{9}

Subtract

x

from both sides

x + x - x = 1 - 2 x + x - x

Simplify

x = 1 - 2 x

Move

2 x

to the left side

3 x = 1

Divide both sides by

3

x = \frac{1}{3}

Verify Solutions:

x = \frac{1}{9}

True

The solution is

x = \frac{1}{9}

x^{2} + 5 x + 20 = 4

2 x - 7 = 13

3 x = 5 x + 4 - 2

- x - 2 - x^{2} = 0

y, x = - y^{2}

What is the answer to sqrt(x)+sqrt(x+\sqrt{x)}=1 ?
The answer to sqrt(x)+sqrt(x+\sqrt{x)}=1 is x= 1/9
Solve for x: sqrt(x)+sqrt(x+\sqrt{x)}=1
The solution is x= 1/9