ASAP. Solve the following equation in the form au^2+bu+c=0 where u is an expression of some variables where a is not equal to 0.

1.  3x^(2/3)+4x^(1/3)-4=0

Let u = x^(1/3).  The equation above becomes

3u^2 + 4u - 4 = 0

This can be factored as

(3u - 2)(u + 2) = 0

so u = 2/3 and u = -2

Because u = x^(1/3) we must have x = u^3 so

x = (2/3)^3 = 8/27   and  x = (-2)^3 = -8

2. (1+1/x)^2 - 6(1+1/x) + 8 =0

Let u = 1+1/x. The equation becomes

u^2 - 6u + 8 = 0

This can be factored as

(u - 4)(u - 2) = 0

so u = 4 and u = 2

Since u = 1 + 1/x  we must have x = 1/(u-1) so

x = 1/(4 - 1) = 1/3  and  x = 1/(2 - 1) = 1

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Hi youngzone,

Whatever happened to 'please'.    Plus, I think that your pirst expression is missing and x

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