SOLUTION: sum of the solutions to the equation (6x-2)^.5 - (4x-3)^.5 = 1 is a) 7 b) 5 c) 4 d) 3

Algebra ->  Equations -> SOLUTION: sum of the solutions to the equation (6x-2)^.5 - (4x-3)^.5 = 1 is a) 7 b) 5 c) 4 d) 3       Log On


   

Question 77272: sum of the solutions to the equation
(6x-2)^.5 - (4x-3)^.5 = 1 is
a) 7
b) 5
c) 4
d) 3
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
(6x-2)^.5 - (4x-3)^.5 = 1
sqrt%286x+-+2%29+-+sqrt%284x+-+3%29+=+1
sqrt%286x+-+2%29+=+1+%2B+sqrt%284x+-+3%29
%28sqrt%286x+-+2%29%29%5E2+=+%281+%2B+sqrt%284x+-+3%29%29%5E2
6x+-+2+=+1+%2B+2%2Asqrt%284x+-+3%29+%2B+4x+-+3
6x+-+4x+-+2+%2B+3+-+1+=+1+-+1+%2B+2%2Asqrt%284x+-+3%29+%2B+4x+-+4x+-+3+%2B+3
2x+=+2%2Asqrt%284x+-+3%29
2x%2F2+=+2%2Asqrt%284x+-+3%29%2F2
x+=+sqrt%284x+-+3%29
%28x%29%5E2+=+%28sqrt%284x+-+3%29%29%5E2
x%5E2+=+4x+-+3
x%5E2+-+4x+%2B+3+=+0
%28x+-+3%29%28x+-+1%29+=+0
x = 3 and x = 1
Sum Solutions: 3 + 1 = 4