CPhill

1. 3x^(2/3)+4x^(1/3)-4=0    I re-wrote this to what I think you meant

Factoring directly, we have

(3x^(1/3) - 2) (x^(1/3) + 2) = 0

Setting each factor to 0, we have

3x^(1/3) - 2 =0   add 2 to both sides

3x^(1/3) = 2    divide by 3 on both sides

x^(1/3) = 2/3   cube both sides

x = 8/27

And for the other factor, we have

x^(1/3) + 2 = 0

Subtract 2 from both sides

x^(1/3) = -2   cube both sides

x = -8

2. (1+1/x)^2 - 6(1+1/x) + 8 =0

We can factor this directly, too

[(1 + 1/x) - 4] [(1 + 1/x) - 2] = 0

Set each factor to 0

(1 + 1/x) - 4 = 0   add 4 to both sides

1 + 1/x = 4          subtract 1 from both sides

1/x = 3               divide by 3 and multiply by x on both sides

x = 1/3

And for the other factor, we have

(1 + 1/x) - 2 = 0   add 2 to both sides

1 + 1/x = 2    subtract 1 from both sides

1/x = 1          so x = 1

3/3 = 1 or 100% ...... The values for 1/3 and 2/3 are decimal approximations.

We can actually use a trick here to factor this as a sum of cubes.

x^4 + y^6   =  (x^4/3)^3 + (y^2)^3....so we have

[x^(4/3) + y^(2)] [x^(8/3) - x^(4/3)y^(2) + y^(4)]

However, the first term could also be factored as a sum of cubes......and we could probably continue this process forever!!!!

One method is to just select a value for x and substitue it into the equation to  find y.

Then, select another value for x and substitute that into the equation to find a second y.

Plot both points on a graph and draw a line between them.

Hint.... ( I might use 0 and 1 for the two x values to substitute)....post back if you have trouble

6 = a(1-5)(1+3)    simplify

6 = a(-4)(4)

6 = a (-16)     divide both sides by -16

-6/16 = a = -3/8

Using

-52 = -4.9t^2    divide both sides by -4.9

10.61 = t^2

3.26 = t

So   v*t =  (7.6m/s)(3.26)s = 24.78m

To find the geometric mean of n numbers, we take the nth root of their product.

So we have......

√(8*18) = √144 = 12

Good job....you are correct....

I think someone is just pulling our leg, Alan.......then again, this could be a part of the "New Math"

3 in 3+4 in b........so we have

ln 3³ + ln b⁴  =

ln 27 + ln b⁴ =

ln 27b⁴