Minimize F = x2 + y2 with x + 2y = 5

Question

Thank you

Answer 1

F = (5-2y)^2 + y^2
= 25-20y+4y^2+y^2
= 5y^2-20y+25
= 5(y^2-4y+5)

y^2-4y+25 = (y-2)^2 + 21
so has minimum at y=2

so, x=1 and

F(1,2) = 5