Question

Solve. Check for extraneous solutions.

1) (/3x+7) = x-1


2) (3/2x)-3=9




Note: (/3x+7) is the square root of 3x plus 7 and (3/2x)-3=9 is 3 times the square root of 2x - 3 equals 9.

Answer 1

1. sqrt(3x+7) = x-1.
Square both sides:
3x + 7 = x^2 - 2x + 1.
-x^2 + 2x +3x = 1 - 7 = - 6.
Multiply both sides by -1:
x^2 -2x -3x = 6.
x^2 - 5x - 6 = 0.
(x+1)(x-6) = 0.

x+1 = 0.
X = -1. Does not satisfy original Eq.

x-6 = 0.
X = 6.

2. 3*sqrt(2x) - 3 = 9.
3*sqrt(2x) = 9+3 = 12.
Divide both sides by 3:
sqrt(2x) = 4.
Square both sides:
2x = 16.
X = 8.