math
posted by cheyanne on .
Solve. Check for extraneous solutions.
1) (/3x+7) = x1
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.

1. sqrt(3x+7) = x1.
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)(x6) = 0.
x+1 = 0.
X = 1. Does not satisfy original Eq.
x6 = 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.