Posted by **Mellie** on Friday, January 7, 2011 at 6:05pm.

The only solution to sqrt (2x+3) - sqrt(x+1) = 1 is x = 3

I think that is true but I'm not sure if I was suppose to separate this equation I just put the 3 in the place of the x and it was true but should I have done it differently?

- Algebra -
**helper**, Friday, January 7, 2011 at 6:42pm
The answer is 3 and -1, from Wolframealpha

I arrived at the - 1 answer, but not sure if the way I solved it is correct and just luck that I got the correct answer of -1!!

maybe a tutor will step in an answer.

- Algebra -
**Reiny**, Friday, January 7, 2011 at 6:44pm
x = 3 does not satisfy the equation as a solution.

LS = (6+3) - √4

= 9-2

= 7

RS = 1

LS ≠ RS, so x ≠ 3

let's solve it ...

(2x+3) - sqrt(x+1) = 1

2x + 3 - 1 = √(x+1)

2x+2 = √(x+1)

square both sides

4x^2 + 8x + 4 = x+1

4x^2 + 7x + 3 = 0

(x+1)(4x+3) = 0

x = -1 or x = -3/4

if x = -1

LS = (-2+3) - √0

= 1-0 = 0

= RS

if x = -3/4

LS = 2(-3/4) + 3 - √(1/4)

= 3/2 - 1/2 = 1

= RS

so x = 0 or x = -3/4

- ARGHH! Algebra -
**Reiny**, Friday, January 7, 2011 at 6:47pm
Forget about my solution above,

Just plain ol' did not see that first square root sign!

- 2nd try .... Algebra -
**Reiny**, Friday, January 7, 2011 at 6:53pm
√(2x+3) = √(x+1) + 1

square both sides

2x+3 = x+1 + 2√(x+1) + 1

x + 1 = 2√(x+1)

square again ...

x^2 + 2x + 1 = 4(x+1)

x^2 - 2x - 3 = 0

(x+1)(x-3) = 0

x = -1 or x = 3

checking both,since we squared.

if x = -1

LS = √(-2+3) - √0

= √1-√0 = 1 = RS

if x = 3

LS = √9 - √4

= 3-2

= 1 = RS

So x = -1 or x = 3

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