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?
Answer:
X=3, y=5
Step-by-step explanation:
3x + y = 14 equation 1
y=5 equation 2
3x + 5 = 14. substitute value of y from equation 2 into equation 1
3x=9
x-3
Start with
Divide both sides by -3
If the absolute value of a number is 4, that number can either be 4 or -4: we have the two solutions
(3/5 + -1/4)/(7/10)
get a common denominator of 20
3/5 * 4/4 =12/20
-1/4 * 5/5 = -5/20
7/10 *2/2 = 17/20
replace
(12/20 - 5/20)/(14/20)
add the top
(7/20)/(14/20)
copy dot flip
7/20 * 20/14
7/14
1/2
Answer: is 5.2
Step-by-step explanation:
you add 8+1+5+0+12 and you then divide it by 5 and you get 5.2
