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

The answer to sqrt(1+\sqrt{x)}=x is x\approx 1.49021…

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

1 + x = x

x \approx 1.49021 \dots

Solution steps

1 + x = x

Remove square roots

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

Solve

x = x^{4} - 2 x^{2} + 1 : x \approx 1.49021 \dots, x \approx 0.52488 \dots

x \approx 1.49021 \dots, x \approx 0.52488 \dots

Verify Solutions:

x \approx 1.49021 \dots

True

, x \approx 0.52488 \dots

False

The solution is

x \approx 1.49021 \dots

1 - \frac{9}{x ^{\frac{2}{3}}} = 0

\frac{4}{4 x + 6} = 2

m + 3 - 2 = 9

x - 10 = 0

\frac{- 3 x + 18}{2 9 - x} = 0

What is the answer to sqrt(1+\sqrt{x)}=x ?
The answer to sqrt(1+\sqrt{x)}=x is x\approx 1.49021…
Solve for x: sqrt(1+\sqrt{x)}=x
The solution is x\approx 1.49021…