What is the only pair of integers (x, y) for which twice the square of the first equals three times the square of the second?
2006-11-19 02:48:09 · 6 answers · asked by Sasha 2 in Science & Mathematics ➔ Mathematics
2x^2 = 3y^2
x^2 = 3/2 y^2
y should be a pair number so that x would be always an integer
and 3/2 y^2 should be a perfect square number too
but there is no two numbers that can fit this profile except (0,0)
2006-11-19 03:06:02 · answer #1 · answered by Anonymous · 0⤊ 0⤋
If there is only one pair of integers it would have to be (0,0) since any other values would work if the integer were positive or negative, since they are squared.
2006-11-19 10:54:24 · answer #2 · answered by hayharbr 7 · 0⤊ 0⤋
2x^2 = 3y^2
x^2 = (3/2)y^2
x/y = sqrt(3/2)
x = 1,224,744,871
y = 1,000,000,000
This is as close as you need.
x^2 = 1.5 * 10^18
y^2 = 1.0 * 10^18
Twice x^2 and 3 times y^2 each equal 3 * 10^18.
2006-11-19 10:59:42 · answer #3 · answered by ? 6 · 0⤊ 0⤋
I can think nothing more than
(0,0)
2006-11-19 10:56:07 · answer #4 · answered by Dupinder jeet kaur k 2 · 0⤊ 0⤋
off the top of my head, (1,1) ?
2006-11-19 10:50:02 · answer #5 · answered by Amy227 2 · 0⤊ 0⤋
(3,2) duh! or (-3, -2)
2006-11-19 11:06:33 · answer #6 · answered by bball_playa 1 · 0⤊ 0⤋