Could you please help me solve these 3? The total assignment is 16 questions but these are the 3 troubling me.
1)
x^2/3 + 3x^1/3 - 18 = 0
Solution set is ( , )
2)
(1/y-9)^2 + 4(1/y-9) - 21 = 0
3)
a= x^2 + 16x -7
( , )
Could you please help me solve these 3? The total assignment is 16 questions but these are the 3 troubling me.
1)
x^2/3 + 3x^1/3 - 18 = 0
Solution set is ( , )
2)
(1/y-9)^2 + 4(1/y-9) - 21 = 0
3)
a= x^2 + 16x -7
( , )
You can convert this to quadratic "form":
. . . . .$\displaystyle \left(x^{\frac{1}{3}}\right)^2\, +\, 3\left(x^{\frac{1}{3}}\right)\, -\, 18\, =\, 0$
Factor this quadratic, and then solve the two exponential equations which result.
This is the same sort of thing, except that the resulting equations will be rational equations.
. . . . .$\displaystyle \left[\left(\frac{1}{y\, -\, 9}\right)\, +\, 7\right]\left[\left(\frac{1}{y\, -\, 9}\right)\, -\, 3\right]\, =\, 0$
All you can do with this one, since you don't have a value for "a", is to move the unknown over to the right-hand side:
. . . . .$\displaystyle 0\, =\, x^2\, +\, 16x\, -\, 7\, -\, a$
Then apply the Quadratic Formula, with the Formula's a = 1, b = 16, and c = -7 - a. (The two a's are different, obviously.)
If you get stuck, please reply showing how far you have gotten. Thank you!