Question

solve the following equation
$12 + 9\sqrt{(x - 1)(3 x + 2) } = 3 {x}^{2} - x$

Answer 1

Final Answer : x = 6 or -17/3

Steps:
1) Let 3x^2-x-2 = t,
then we get
=> 12 + 9√t = t + 2. -----(1)
=>9√t = t -10
Square both sides.

2) Then,
obtain values of t from above quadratic equation and check whether they satisfy equation (1) or not.
t = 1 does not satisfy and t = 100 satisfy.

3) Substitute value of t , in t = 100
From, here we get
x = 6 or x = -17/3


For Calculation see pic.