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

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√1+4√x=√x+1

Solution

x=4, x=0

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Solution steps

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√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=x2

Square both sides: x=x²4

x=x²4

Solve x=x²4 : x=4, x=0

x=4, x=0

Verify Solutions: x=4 True, x=0 True

The solutions are

x=4, x=0

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

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

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