Shameilia wrote:I factored out the quadratic equation in the exponents. I got the following:
(2X-2)(X-1) (1,1)
(3X+6)(X-2) (-2, 2)
From there I multiplied the 1 x 1 x -2 x 2 = -4.
I selected answer C.
Was my path to the correct answer by chance?
(Note: I'm going to break this up into parts, since it has a few neat twists and also is a bit too long for one post.)
There was some luck involved there, but as they say in poker, better lucky than good!
You could start by
dividing both sides by the right hand side, giving
(x²)^(x² - 2x + 1) / x^(3x² + x + 8) = 1
Now let's distribute the 2 in the numerator on the left:
(x)^(2x² - 4x + 2) / x^(3x² + x + 8) = 1
Then we'll apply our exponent property, xᵃ/xᵇ = xᵃ�ᵇ:
x^(2x² - 4x + 2 - (3x² + x + 8)) = 1
x^(-x² - 5x - 6) = 1
Since the right hand side, 1, is the same as x�,
we can say
x^(-x² - 5x - 6) = x�
and that
-x² - 5x - 6 = 0
0 = x² + 5x + 6
0 = (x + 2) * (x + 3)
So it looks like x = -2 and x = -3 are the solutions, but did you notice my mistake?
