Let $a,$ $b,$ $c$ be real numbers such that $a + b + c = 1.$  Find the minimum value of $2a^2 + 3b^2 + 6c^2.$
from sympy import Symbol, solve

a = Symbol('a')
b = Symbol('b')
c = Symbol('c')

eq1 = a + b + c - 1

eq2 = 2*a**2 + 3*b**2 + 6*c**2

a_1, b_1, c_1 = solve ( eq1, (a, b, c) )[0]

answer = eq2.subs( [ (a, a_1), (b, b_1), (c, c_1) ] )

print(answer)