What is the answer to a=sqrt(4+\sqrt{5+a)} ?

The answer to a=sqrt(4+\sqrt{5+a)} is a\approx 2.59936…

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a=sqrt(4+\sqrt{5+a)}

a = 4 + 5 + a

a \approx 2.59936 \dots

Solution steps

a = 4 + 5 + a

Remove square roots

a^{4} - 8 a^{2} + 16 = 5 + a

Solve

a^{4} - 8 a^{2} + 16 = 5 + a : a \approx 2.59936 \dots, a \approx - 2.37095 \dots, a \approx 1.22665 \dots, a \approx - 1.45505 \dots

a \approx 2.59936 \dots, a \approx - 2.37095 \dots, a \approx 1.22665 \dots, a \approx - 1.45505 \dots

Verify Solutions:

a \approx 2.59936 \dots

True

, a \approx - 2.37095 \dots

False

, a \approx 1.22665 \dots

False

, a \approx - 1.45505 \dots

False

The solution is

a \approx 2.59936 \dots

1 + 2 = a - 1

x + 3 + 4 = 5

0.75 = 2 π \frac{8}{k}

x^{2} + 1 = - x^{2} + 5

11 y + 9 - y + 4 = 5

What is the answer to a=sqrt(4+\sqrt{5+a)} ?
The answer to a=sqrt(4+\sqrt{5+a)} is a\approx 2.59936…
Solve for a: a=sqrt(4+\sqrt{5+a)}
The solution is a\approx 2.59936…