SOLUTION: how do you solve the radical equation radical sign(x-2) + 3 = radical sign (4x+1)

Algebra ->  Radicals -> SOLUTION: how do you solve the radical equation radical sign(x-2) + 3 = radical sign (4x+1)       Log On


   

Question 109418: how do you solve the radical equation
radical sign(x-2) + 3 = radical sign (4x+1)
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
radical sign(x-2) + 3 = radical sign (4x+1)
Square both sides to get:
(x-2) + 6sqrt(x-2)+9 = 4x+1
x+7 + 6sqrt(x-2) = 4x+1
6sqrt(x-2) = 3x-6
Divide thru by 3 to get:
2sqrt(x-2) = x-2
Square both sides to get:
4(x-2) = x^2-4x+4
4x-8 = x^2-4x+4
x^2-8x+12 = 0
(x-2)(x-6)=0
x = 2 or x=6
-------------
Check these answers in sqrt(x-2) + 3 = sqrt(4x+1)
Check x=2:
sqrt(0)+3 = sqrt(9)
True
---------------
Check x=6:
sqrt(4) + 3 = sqrt(25)
True
------------------
Both solutions are good.
===============
Cheerd,
Stan H.