Please help?

Question

please show steps of solving this problem especially the second part.
http://aycu10.webshots.com/image/36729/2005287368351421111_rs.jpg

Answer 1

For this problem you have to find the least common den. of 2, 12, 18
To do this first split 12 into its prime roots
They are (2),(2), and (3)
Then do this for 18
They are (2)(3)(3)
Then do this for 2
It is just (2)
Then you can get rid of any prime number which appears in all 3 numbers (get rid of a 2 in each)
Then multiply all those numbers together
This is (1)(2)(2)(3)(3)=36
so the answer is 36

Answer 2

The equation is
x³ -1/2 x² + 1/12 x + 1/18 = 0.
Let x = y / λ and Then y = λx.
Substituting, we get
y³/ λ³ - 1/2 y²/λ² + 1/12 y/λ + 1/18 = 0.
Clearing denominators, we get
y³ - 1/2 y²λ + 1/12 yλ² + λ³/18 = 0. (*)
That's the answer to part 1.
The answer to the second part is 6.
No smaller positive integer works and
if we replace λ by 6 in (*) we get
y³ -3y² + 3y + 12 = 0.

Answer 3

Use Cardan's formula (the only way to solve cubic):

http://www-history.mcs.st-andrews.ac.uk/HistTopics/Quadratic_etc_equations.html