how do i solve the equation x*y*z = 150 where y=2x and z=(x-2) ?
substitute for y and z into the 1st expression.
x*(2x)*(x-2) = 150
2x^3 - 4x^2 - 150 = 0
By inspection, x = 5 is a root, hence (x - 5) is a factor. Taking out this factor gives us,
(x - 5)(2x^2 + 6x + 30) = 0
(x - 5)(x^2 + 3x + 15) = 0
The discriminant for the quadratic is D = 3^2 - 4*1*15 = 9 - 60 = -51.
Since the discriminant is < 0, then there are no real roots.
The only solution is the root: x = 5