SOLUTION: The number of solutions for square root of (5x+7) - sq. root of (3x+1) = sq. root of (x+3)

Question 752189: The number of solutions for square root of (5x+7) - sq. root of (3x+1) = sq. root of (x+3)
Answer by malglu(63) (Show Source): You can put this solution on YOUR website!
what you need to do is square each side of the equation to get rid of the roots. you will need to do this twice
first time
(sqrt (5x+7) -sqrt (3x+1)) ^2 = sqrt (x+3)^2
multiply out the brackets to get
5x+7 -2sqrt (3x+1)(5x+7) + 3x+1 =x+3
put the sqrt expression on one side of the = sign to get
7x+5 = 2 sqrt (3x+1)(5x+7)
now square each side again
(7x+5) (7x+5) = 2^2 (sqrt (3x+1)^2) (sqrt (5x+7)^2)
49x^2 +70x +25 = 4 (3x+1) (5x+7)
11x^2 -38x +3 +0
use the formula to solve this
i am in a bit of a rush so cannot check my arithmatic, but the method should be correct.
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