Surds
posted by Gingie on .
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.......??????????

Whoops I meant ..
Sqrt of x+3, not x+1.. 
(a+b)^2 = a^2 + ab + b^2

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^220x12=0
(5x+2)(5x6)=0
x=12/5 or x=6/5
check that. 
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)(x6) = 0
x = 2/9 , 6
But x=6 does not satisfy the original equation, so 2/9 is the only solution.