Question

Medal!!!!!!!!!!!
Historical Feature:
In the equation x^3+px+q=o, replace x by H+K. Let 3HK=-p, and show that H^3+K^3=-q

Answer 1

$$
\Large{ x^3+px+q=0
\\ x= h+k
\\ 3hk=-p
\\~\\ \textrm{Our goal is show that} ~h^3+k^3=-q
\\ \textrm{Steps: substitute}
\\~\\ (h+k)^3 + (-3hk)(h+k) + q=0

}
$$

Answer 2

can you expand that?

Answer 3

q=-h^3-k^3

Answer 4

thats what you need to show

Answer 5

wait what