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

The answer to sqrt(1+4\sqrt{x)}=sqrt(x)+1 is x=4,x=0

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sqrt(1+4\sqrt{x)}=sqrt(x)+1

1 + 4 x = x + 1

x = 4, x = 0

Solution steps

1 + 4 x = x + 1

Square both sides:

1 + 4 x = x + 2 x + 1

1 + 4 x = x + 2 x + 1

Subtract

1

from both sides

1 + 4 x - 1 = x + 2 x + 1 - 1

Simplify

4 x = x + 2 x

Move

2 x

to the left side

2 x = x

Divide both sides by

2

x = \frac{x}{2}

Square both sides:

x = \frac{x ^{2}}{4}

x = \frac{x ^{2}}{4}

Solve

x = \frac{x ^{2}}{4} : x = 4, x = 0

x = 4, x = 0

Verify Solutions:

x = 4

True

, x = 0

True

The solutions are

x = 4, x = 0

5 x + 6 + 3 = 3 x + 3 + 4

(4 x - 16)^{\frac{1}{2}} = 36

9 - x + 2 = x - 5

5 x - 26 + 4 = x

5 x + 19 - 5 x = - 1

What is the answer to sqrt(1+4\sqrt{x)}=sqrt(x)+1 ?
The answer to sqrt(1+4\sqrt{x)}=sqrt(x)+1 is x=4,x=0
Solve for x: sqrt(1+4\sqrt{x)}=sqrt(x)+1
The solution is x=4,x=0