2006-08-13 06:08:09 · 16 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
When there are two variables at least two equations must be given to find the values.
In this case where only one equaton is given
x=514 & y = 1
OR
x=1 & y= 514
2006-08-13 06:56:30 · answer #1 · answered by tuhinrao 3 · 0⤊ 0⤋
x = 1 or 514
y = 514 or 1
2006-08-13 13:16:16 · answer #2 · answered by shmifty__14 5 · 1⤊ 0⤋
It is impossible to completely solve it. You can solve for y in terms of x, or x in terms of y, but you cannot find both x and y.
The rule is, to solve for n variables, you need n equations. Here, you have 2 variables, and 1 equation. Thus, you cannot solve for x and y.
edit:
And no, to those saying either x = 1 and y = 514, or x = 514 and y = 1, this is not the answer. There are infinite answers to this problem, those you've presented are simply two out of the infinite answers.
and you can't arbitrarily make a restriction to N either...wow.
2006-08-13 13:15:21 · answer #3 · answered by a_liberal_economist 3 · 0⤊ 0⤋
I don't know who taught you math, but this is a hard question. You have one equation and two unknowns, and as such, there are an infinate number of possible solutions for x and y. For example,
y = 514, x =1 is a possible solution.
y = 1, x =514 is another possible solution.
y = 2, x = 4.60144843 is correct to 6 decimal places, but is not exact.
To find exact values, you need another equation, such as (x^y)(y^x) = 784. Then there would be finite solutions to both x and y.
2006-08-13 13:25:42 · answer #4 · answered by Paul W 2 · 0⤊ 0⤋
x=514 and y=1
or
x=1 and y=514
2006-08-16 07:36:01 · answer #5 · answered by Jangid 3 · 0⤊ 0⤋
x=514 or 1
y=1 or 514
2006-08-16 02:43:56 · answer #6 · answered by ankuC2500 1 · 0⤊ 0⤋
x^y*y^x=514
x=514 and y=1 or the other way about
2006-08-13 13:15:06 · answer #7 · answered by raj 7 · 0⤊ 0⤋
While it is true that there are an infinte number of solutions if x and y are real (and positive) i presume there is a restriction to integers
obviously (x,y) = (514,1) or (1,514) are solutions. But are there others?
514 = 2 * 257
Since x and y are integers then x^y is and integer and y^x is an integer.
Also that implies that x^y is one of 1,2,257,514 and y^x is one of 514,257,2,1
But for our non-trivial solutions that would mean either x^y is 2 or y^x is 2.
This clearly is impossible with two integers. Thus the trivial (1,514) solution is the only integer solution.
2006-08-13 14:06:13 · answer #8 · answered by Anonymous · 0⤊ 1⤋
To find the values for X and Y, u need atleast 2 equations or 2 sets of relations. since only one set of relation is given, there are infinite number of solutions to this problem
2006-08-13 13:25:18 · answer #9 · answered by arvind k 1 · 0⤊ 0⤋
If you have only one equation you have an infinite number of solutions...
2006-08-13 14:13:05 · answer #10 · answered by None A 3 · 0⤊ 0⤋