For the first one :
Let A(a), B(b) and C(c)
Let I be the middle of [AB]
ABC being equilateral
I've got 2 exercises I can't solve.
The first one is :
If a,b,c ∈ C and they are affix points of the plan.
Show that the triangle ABC is equilateral only if
a^2+b^2+c^2 = ab+ bc + ca
The second one is to demonstrate that :
X^4 + 2X^3 + 4X^2 + 2X + 3
has no square root in R.
I'm looking forward to your answers,
PS : Sorry for my bad english