8, x, y, 24

Question

The first three terms are geometric.
The last three terms are arithmetic.
Find x and y.

Answer 1

x^2 = 8y
y-x = 24-y
solve to get
8, -8, 8, 24
or
8, 12, 18, 24

Answer 2

relation #1:
x-8 = y-x
y = 2x - 8

relation #2:
y/x = 24/y
y^2 = 24x or x = y^2/24

substitution
y = 2(y^2/24) - 8
12y = y^2 - 96
y^2 - 12y - 96 = 0
solving using the formual I get
x = 7-√33, y = 6 - 3√33
or
x = 7 + √33, y = 6 + 2√33

both case work.
I was expecting some rational answers, are you sure
the question was posted corrrectly?

Answer 3

arggghhhh!
got the whole thing backwards, go with oobleck

(it was still fun doing it the wrong way)