What is the answer to sqrt(x+\sqrt{x+\sqrt{x)}}=2 ?

The answer to sqrt(x+\sqrt{x+\sqrt{x)}}=2 is x\approx 2.11185…

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sqrt(x+\sqrt{x+\sqrt{x)}}=2

x + x + x = 2

x \approx 2.11185 \dots

Solution steps

x + x + x = 2

Remove square roots

x = x^{4} - 18 x^{3} + 113 x^{2} - 288 x + 256

Solve

x = x^{4} - 18 x^{3} + 113 x^{2} - 288 x + 256 : x \approx 2.11185 \dots, x \approx 2.90445 \dots, x \approx 5.85303 \dots, x \approx 7.13065 \dots

x \approx 2.11185 \dots, x \approx 2.90445 \dots, x \approx 5.85303 \dots, x \approx 7.13065 \dots

Verify Solutions:

x \approx 2.11185 \dots

True

, x \approx 2.90445 \dots

False

, x \approx 5.85303 \dots

False

, x \approx 7.13065 \dots

False

The solution is

x \approx 2.11185 \dots

3 x + 2 = 11

w = 108 w

x - 2 - x + 3 = 1

4 x^{2} - 15 - 2 x = - 1

y, x = 16 - y^{2}

What is the answer to sqrt(x+\sqrt{x+\sqrt{x)}}=2 ?
The answer to sqrt(x+\sqrt{x+\sqrt{x)}}=2 is x\approx 2.11185…
Solve for x: sqrt(x+\sqrt{x+\sqrt{x)}}=2
The solution is x\approx 2.11185…