What is the answer to x^2=sqrt(x)+1 ?

The answer to x^2=sqrt(x)+1 is x\approx 1.49021…

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x^2=sqrt(x)+1

x^{2} = x + 1

x \approx 1.49021 \dots

Solution steps

x^{2} = x + 1

Remove square roots

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

Solve

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

27 - 2 x = x - 3

w = 9 w - 18

(x + 2) (x - 2) = 0

x, y = 14 x

6 x + 2 = 7 x

What is the answer to x^2=sqrt(x)+1 ?
The answer to x^2=sqrt(x)+1 is x\approx 1.49021…
Solve for x: x^2=sqrt(x)+1
The solution is x\approx 1.49021…