What is the answer to a=sqrt(a-2\sqrt{a-1\sqrt{a)}} ?

The answer to a=sqrt(a-2\sqrt{a-1\sqrt{a)}} is a=0,a=1

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a=sqrt(a-2\sqrt{a-1\sqrt{a)}}

a = a - 2 a - 1 a

a = 0, a = 1

Solution steps

a = a - 2 a - 1 \cdot a

Remove square roots

a^{8} - 4 a^{7} + 6 a^{6} - 12 a^{5} + 17 a^{4} - 8 a^{3} + 16 a^{2} = 16 a

Solve

a^{8} - 4 a^{7} + 6 a^{6} - 12 a^{5} + 17 a^{4} - 8 a^{3} + 16 a^{2} = 16 a : a = 0, a = 1, a \approx 2.58444 \dots, a \approx 1.74649 \dots

a = 0, a = 1, a \approx 2.58444 \dots, a \approx 1.74649 \dots

Verify Solutions:

a = 0

True

, a = 1

True

, a \approx 2.58444 \dots

False

, a \approx 1.74649 \dots

False

The solutions are

a = 0, a = 1

3 - 3 x = x + 5

3 x + 16 = 2 x - 1

x - 2 x - 8 = 0

3 x + 7 - x + 1 = 2

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

What is the answer to a=sqrt(a-2\sqrt{a-1\sqrt{a)}} ?
The answer to a=sqrt(a-2\sqrt{a-1\sqrt{a)}} is a=0,a=1
Solve for a: a=sqrt(a-2\sqrt{a-1\sqrt{a)}}
The solution is a=0,a=1