Ax
y = 7Ax y-1
6Cx
y = 5Cx y+1
Astfel =>
y ≤ x
y-1 ≤ x
y+1 ≤ x
Ax
y = 7Ax y-1 = x! / (x-y)! = 7 * x!
/ (x-y+1)!
1 / (x-y)!
= 7 / (x-y+1)! * (x– y+1)
x– y+1 = 7
x - y = 6
6Cx
y = 5Cx y+1
6 * x! / y! (x - y)! = 5 * x! / (y+1)!(x-y-1)!
scriem pe (x - y)! ca (x-y-1)!
*(x-y)
iar (y+1)! ca y!*(y+1)
*(y+1) *(x-y)
6 / y! (x-y-1)!(x - y) = 5 / y!(y+1)(x-y-1)!
eliminam numitorul si =>
6y + 6 = 5x – 5y
5x - 11y = 6
Din ambele ecuatii=>
x - y = 6 /* (-5)
5x - 11y = 6
16y = -24
y = -24 / 16
y = -3 / 2 nu € N