If a,b are the roots ( assumed non 0 ) of 3x^2-4x+1=0 form the equation whose roots are a^2/b and b^2/a.

If a and b are  the roots of the given equation, then,
using Viete's relationships, we could write:

a+b = -
(-4)/3

a*b = 1/3

Now, we know
that we could write an equation if we know the sum and the product of it's
roots:

x^2 - Sx + P = 0

We
know that the roots of the equation we have to form are: a^2/b and
b^2/a.

We'll write the sum of
them:

S = a^2/b + b^2/a = (a^3 +
b^3)/a*b

But the sum of cubes from numerator could be
written as:

a^3 + b^3 = (a+b)^3 -
3a*b(a+b)

We'll substitute in the relation above, the
values of a+b and a*b:

(a+b)^3 - 3a*b(a+b) = (4/3)^3-
3*(1/3)(4/3) = (4/3)(16/9 - 1)

a^3 + b^3 = (4/3)*(7/9) =
28/27

S =
(28/27)/(1/3)

S =
28/9

P = (a^2/b)* (b^2/a) 
=a*b = 1/3

The quadratic equation whose
roots are  (a^2/b) and (b^2/a) is:

x^2 - (28/9)*x + 1/3 =
0

9x^2 - 28x + 3 =
0