Question

suppose x and y are integers with 2x+y=30. Find the minimum value of x^2 +y

Answer 1

the answer is 29. I just dont understand why

Answer 2

Ever hear of Lagrange multipliers?

Answer 3

no

Answer 4

simple substitution and then find vertex

Answer 5

nope

Answer 6

\[y=30-2x\]\[ x^2+y =x^2-2x+30\] vertex at 1

\[1^2-2\cdot 1+30=29\]

Answer 7

how did you get x^2+y =x^2-2x+30

Answer 8

replace y with \[y=30-2x=-2x+30\]

Answer 9

ohhh wow okay I understand!

Answer 10

Thank you both @Zarkon @IrishBoy123!!!