Is there any pair of numbers whose product is the same as its sum?
Thank you for the help :)
3 and 1.5
xy = x+y
xy - y = x
y(x-1) = x
y = x/(x-1)
x -- y
5 .. 5/4
4 .. 4/3
3 .. 3/2
2 .. 2
There is an infinite pair of such numbers , but the only two integers where this happens is for the numbers 2 and 2
2+2 = 4
2x2 = 4
notice this is also true for any of the above non-integer pairs.
5 + 5/4 = 6.25
5(5/4) = 25/4 = 6.25
etc
To find out if there is any pair of numbers whose product is the same as its sum, we can start by assuming the two numbers are x and y.
The product of the two numbers can be written as x * y, and the sum can be written as x + y.
So, we need to find a pair of numbers where x * y is equal to x + y.
To simplify the problem, we can rearrange the equation to get x * y - x - y = 0.
Next, we can factor the equation by grouping: x * (y - 1) - (y - 1) = 0.
We now have (x - 1)(y - 1) = 1.
To find the pair of numbers, we need to find two integers (x - 1) and (y - 1) whose product is equal to 1.
Since the product of two integers can only be equal to 1 if both integers are 1 or -1, we have the following possibilities:
Case 1: (x - 1) = 1, (y - 1) = 1
In this case, x = 2, and y = 2.
Case 2: (x - 1) = -1, (y - 1) = -1
In this case, x = 0, and y = 0.
Therefore, the two pairs of numbers whose product is the same as their sum are (2, 2) and (0, 0).