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

The answer to sqrt(2+\sqrt{2-\sqrt{2+x)}}=x is x\approx 1.53208…

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

2 + 2 - 2 + x = x

x \approx 1.53208 \dots

Solution steps

2 + 2 - 2 + x = x

Remove square roots

2 + x = x^{8} - 8 x^{6} + 20 x^{4} - 16 x^{2} + 4

Solve

2 + x = x^{8} - 8 x^{6} + 20 x^{4} - 16 x^{2} + 4 : x = - 1, x = 2, x \approx 1.24697 \dots, x \approx 1.53208 \dots, x \approx - 1.87938 \dots, x \approx 0.34729 \dots, x \approx - 0.44504 \dots, x \approx - 1.80193 \dots

x = - 1, x = 2, x \approx 1.24697 \dots, x \approx 1.53208 \dots, x \approx - 1.87938 \dots, x \approx 0.34729 \dots, x \approx - 0.44504 \dots, x \approx - 1.80193 \dots

Verify Solutions:

x = - 1

False

, x = 2

False

, x \approx 1.24697 \dots

False

, x \approx 1.53208 \dots

True

, x \approx - 1.87938 \dots

False

, x \approx 0.34729 \dots

False

, x \approx - 0.44504 \dots

False

, x \approx - 1.80193 \dots

False

The solution is

x \approx 1.53208 \dots

x - 5 + 7 = x

x + 2 = 4

4 x - 2 = 3 x + 13

x^{\frac{2}{3}} = - 36

x + 3 = 8

What is the answer to sqrt(2+\sqrt{2-\sqrt{2+x)}}=x ?
The answer to sqrt(2+\sqrt{2-\sqrt{2+x)}}=x is x\approx 1.53208…
Solve for x: sqrt(2+\sqrt{2-\sqrt{2+x)}}=x
The solution is x\approx 1.53208…