What is the answer to x=sqrt(2022+\sqrt{2022+x)} ?

The answer to x=sqrt(2022+\sqrt{2022+x)} is x\approx 45.46943…

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x=sqrt(2022+\sqrt{2022+x)}

x = 2022 + 2022 + x

x \approx 45.46943 \dots

Solution steps

x = 2022 + 2022 + x

Remove square roots

x^{4} - 4044 x^{2} + 4088484 = 2022 + x

Solve

x^{4} - 4044 x^{2} + 4088484 = 2022 + x : x \approx 45.46943 \dots, x \approx - 44.46943 \dots, x \approx 44.45831 \dots, x \approx - 45.45831 \dots

x \approx 45.46943 \dots, x \approx - 44.46943 \dots, x \approx 44.45831 \dots, x \approx - 45.45831 \dots

Verify Solutions:

x \approx 45.46943 \dots

True

, x \approx - 44.46943 \dots

False

, x \approx 44.45831 \dots

False

, x \approx - 45.45831 \dots

False

The solution is

x \approx 45.46943 \dots

7606 = 552 0^{2} + q^{2}

y, x = y^{\frac{1}{2}}

x^{2} + 3 x + 13 = x - 1

- 6^{2} + 0^{2} = x^{2}

6 - x + x = 0

What is the answer to x=sqrt(2022+\sqrt{2022+x)} ?
The answer to x=sqrt(2022+\sqrt{2022+x)} is x\approx 45.46943…
Solve for x: x=sqrt(2022+\sqrt{2022+x)}
The solution is x\approx 45.46943…