Posted by **Gingie** on Friday, July 11, 2014 at 6:48pm.

Solve in the exact form.

(sqrt of 4x+1)+(sqrt of x+1)=2

Someone showed me to do this next:

Square both sides..so..

4x+1+2((sqrt of 4x+1)•(sqrt of x+1))=4

I do not understand where the 2 come from ..and why do we need to multiply the sqrt of 4x+1 and sqrt of x+1 together to get the product.......??????????

- Surds -
**Gingie**, Friday, July 11, 2014 at 6:49pm
Whoops I meant ..

Sqrt of x+3, not x+1..

- Surds -
**DrBob222**, Friday, July 11, 2014 at 7:26pm
(a+b)^2 = a^2 + ab + b^2

- Surds -
**bobpursley**, Friday, July 11, 2014 at 7:53pm
a+b)^2 = a^2 + 2ab + b^2

(sqrt of 4x+1)+(sqrt of x+3)=2

4x+1 + 2 (sqrt (x+3)sqrt(4x+1)) + x+3=4

5x+4 +2 (sqrt (5x+4)=4

5x+2sqrt(5x+4)=0

5x=-2(sqrt(5x+4)

square both sides

25x^2=4(5x+3)

25x^2-20x-12=0

(5x+2)(5x-6)=0

x=-12/5 or x=6/5

check that.

- Surds -
**Steve**, Friday, July 11, 2014 at 8:44pm
Hmmm. I get

√(4x+1)+√(x+3)=2

4x+1 + 2√(4x^2+13x+3) + x+3 = 4

5x = -2√(4x^2+13x+3)

25x^2 = 4(4x^2+13x+3)

25x^2 = 16x^2 + 52x + 12

9x^2 - 52x - 12 = 0

(9x+2)(x-6) = 0

x = -2/9 , 6

But x=6 does not satisfy the original equation, so -2/9 is the only solution.

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