2006-11-20 12:58:10 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Quite an old example, and one of the best-known, is the so-called Pell equation X^2 - D.Y^2 = -1 or +1, where D is a square-free integer and X, Y are both to be integers. For example, when D = 3, there is no solution when -1 is on the right-hand side, but the solutions when it is +1 are (X, Y) = (2, 1), (7, 4), (26, 15), (97, 56), . . . an infinite series of integer pairs constructed by a simple rule starting from the first one (X' = 2X + 3Y, Y' = X + 2Y).
2006-11-21 04:32:14 · answer #1 · answered by Anonymous · 0⤊ 1⤋
y = 1/x --> x = 1/y
For every value of x, there corresponds a number, y, which is its reciprocal. This implies that for every value of y, there also corresponds a value, x, which is its reciprocal. Since both number lines have an infinite number of elements, then both equations have an infinite number of elements in their solution sets.
2006-11-20 13:22:16 · answer #2 · answered by MathBioMajor 7 · 0⤊ 1⤋
If an equation in 2 variables is OK, then x-y = 1 will do fine.
2006-11-20 13:41:54 · answer #3 · answered by steiner1745 7 · 0⤊ 1⤋
3x/2 + 2y/3 = 25
2006-11-21 03:13:59 · answer #4 · answered by Akilesh - Internet Undertaker 7 · 0⤊ 2⤋
(x+1)/5 = (3x+3)/15
2006-11-20 13:03:37 · answer #5 · answered by hayharbr 7 · 0⤊ 1⤋
x = x
or
2x = 2x
2006-11-20 13:01:06 · answer #6 · answered by chris p 3 · 0⤊ 1⤋
x = [-infinity, +infinity]
2006-11-20 13:08:01 · answer #7 · answered by Jimie 1 · 0⤊ 4⤋