What is the answer to sqrt(5-\sqrt{5-x)}=x ?

The answer to sqrt(5-\sqrt{5-x)}=x is x\approx 1.79128…

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sqrt(5-\sqrt{5-x)}=x

5 - 5 - x = x

x \approx 1.79128 \dots

Solution steps

5 - 5 - x = x

Remove square roots

5 - x = x^{4} - 10 x^{2} + 25

Solve

5 - x = x^{4} - 10 x^{2} + 25 : x \approx - 2.79128 \dots, x \approx 2.56155 \dots, x \approx - 1.56155 \dots, x \approx 1.79128 \dots

x \approx - 2.79128 \dots, x \approx 2.56155 \dots, x \approx - 1.56155 \dots, x \approx 1.79128 \dots

Verify Solutions:

x \approx - 2.79128 \dots

False

, x \approx 2.56155 \dots

False

, x \approx - 1.56155 \dots

False

, x \approx 1.79128 \dots

True

The solution is

x \approx 1.79128 \dots

38 - 8 x^{3} + 71 = 0

x - 3 = x

x - 6 = x + 6

1.2 x = 8 x^{0.12}

2 = 3 u - 12 - 1

What is the answer to sqrt(5-\sqrt{5-x)}=x ?
The answer to sqrt(5-\sqrt{5-x)}=x is x\approx 1.79128…
Solve for x: sqrt(5-\sqrt{5-x)}=x
The solution is x\approx 1.79128…