What is the answer to sqrt(4+\sqrt{23+\sqrt{1+\sqrt{x-3)}}}=3 ?

The answer to sqrt(4+\sqrt{23+\sqrt{1+\sqrt{x-3)}}}=3 is x=12

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sqrt(4+\sqrt{23+\sqrt{1+\sqrt{x-3)}}}=3

4 + 23 + 1 + x - 3 = 3

x = 12

Solution steps

4 + 23 + 1 + x - 3 = 3

Square both sides:

4 + 23 + 1 + x - 3 = 9

4 + 23 + 1 + x - 3 = 9

Move

4

to the right side

23 + 1 + x - 3 = 5

Square both sides:

23 + 1 + x - 3 = 25

23 + 1 + x - 3 = 25

Move

23

to the right side

1 + x - 3 = 2

Square both sides:

1 + x - 3 = 4

1 + x - 3 = 4

Move

1

to the right side

x - 3 = 3

Square both sides:

x - 3 = 9

x - 3 = 9

Solve

x - 3 = 9 : x = 12

x = 12

Verify Solutions:

x = 12

True

The solution is

x = 12

3 x + 4 - 1 = 2 x + 1

x^{2} + 3 x + 5 = 3

3 x + 1 = \frac{3 x}{2} + 1

1 = x^{- \frac{1}{3}}

What is the answer to sqrt(4+\sqrt{23+\sqrt{1+\sqrt{x-3)}}}=3 ?
The answer to sqrt(4+\sqrt{23+\sqrt{1+\sqrt{x-3)}}}=3 is x=12
Solve for x: sqrt(4+\sqrt{23+\sqrt{1+\sqrt{x-3)}}}=3
The solution is x=12