What is the answer to x+sqrt(x+\sqrt{x-1)}=6 ?

The answer to x+sqrt(x+\sqrt{x-1)}=6 is x\approx 3.69100…

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x+sqrt(x+\sqrt{x-1)}=6

x + x + x - 1 = 6

x \approx 3.69100 \dots

Solution steps

x + x + x - 1 = 6

Remove square roots

x - 1 = x^{4} - 26 x^{3} + 241 x^{2} - 936 x + 1296

Solve

x - 1 = x^{4} - 26 x^{3} + 241 x^{2} - 936 x + 1296 : x \approx 3.69100 \dots, x \approx 4.40099 \dots, x \approx 8.37974 \dots, x \approx 9.52825 \dots

x \approx 3.69100 \dots, x \approx 4.40099 \dots, x \approx 8.37974 \dots, x \approx 9.52825 \dots

Verify Solutions:

x \approx 3.69100 \dots

True

, x \approx 4.40099 \dots

False

, x \approx 8.37974 \dots

False

, x \approx 9.52825 \dots

False

The solution is

x \approx 3.69100 \dots

x - 4 = 5

2 x^{- 1} + x^{\frac{- 1}{2}} = 6

(x - 1)^{\frac{3}{4}} = 64

3 x^{2} - 4 3 x + 4 = 0

a - 3 a - 18 = 0

What is the answer to x+sqrt(x+\sqrt{x-1)}=6 ?
The answer to x+sqrt(x+\sqrt{x-1)}=6 is x\approx 3.69100…
Solve for x: x+sqrt(x+\sqrt{x-1)}=6
The solution is x\approx 3.69100…