Answer:
1 1/2 points
Step-by-step explanation:
Set the whole expression = to 0 and solve for x.
3x^(5/3) - 4x^(7/3) = 0. Factor out x^(5/3): x^(5/3) [3 - 4x^(2/3)] = 0
Then either x^(5/3) = 0, or 3 - 4x^(2/3) = 0.
In the latter case, 4x^(2/3) = 3.
To solve this: mult. both sides by x^(-2/3). Then we have
4x^(2/3)x^(-2/3) = 3x^(-2/3), or 4 = 3x^(-2/3). It'd be easier to work with this if we rewrote it as
4 3
--- = --------------------
1 x^(+2/3)
Then
4
--- = x^(-2/3). Then, x^(2/3) = (3/4), and x = (3/4)^(3/2). According to my 3 calculator, that comes out to x = 0.65 (approx.)
Check this result! subst. 0.65 for x in the given equation. Is the equation then true?
My method here was a bit roundabout, and longer than it should have been. Can you think of a more elegant (and shorter) solution?
the discriminant b^2 - 4ac when the equation is in the form of ax^2 +bx+c=0
13x^2-16x = x^2 -x
we need to get in it the standard form
subtract x^2 from each side
12x^2 -16x = -x
add x to each side
12x^2 -15x = 0
12x^2 -15x -0 =0
a=12 b=-15 c=0
b^2 -4ac
the discriminant = b^2
b^2 = (-15)2 = 225
Answer:
Step-by-step explanation:
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