Let's start by simplifying the question:ern5231 wrote:What is the maximum value of x^2+2y^2+5x-35? Given that x2+y2=5.
A.22 B.20 C.0 D.-20 E.-22
x^2 + 2y^2 + 5x - 35
= x^2+ y^2 + y^2 + 5x - 35
Since x^2 + y^2 = 5,
= 5 + y^2 + 5x - 35
= y^2 + 5x - 30
So, that's the expression we want to maximize.
Now let's ask ourselves if we want to equally distribute the 5 to x^2 and y^2 or if we want to stack one of them. To maximize, we're going to want to make one of them as big as possible.
We know the max value for either is root5 (making the other equal 0). What's going to be greater - root5 squared or 5*root5. 5*root5 is going to be bigger, so let's let:
x = root5 and y = 0
However, when we plug in those values we get:
5(root5) - 30
which isn't among the choices (although -20 is the closest).
Is part of the question missing? Do we know that x and y have to be integers? Even if we let x=2 and y=1 we get:
1^2 + 5(2) - 30 = -19, also not among the choices.
