Find the largest constant \(c\) so that
\(x^2 + y^2 + 1 \ge c(x + y)\)
for all real numbers \(x\) and \(y\)
pls i need it done quick
By Lagrange Multipliers, you get the optimal value when x = y = 1:
x^2 + y^2 + 1 >= c(x + y)
3 >= 2c
c <= 3/2
So the largest constant c is 3/2.
For those of us who are unsure, are negative numbers real numbers ?
If that's the case, then if both x and y are negative, c can be as large as you please.
