Tìm các số nguyên x,y sao cho x(y+1)-y=6 10/07/2021 Bởi Samantha Tìm các số nguyên x,y sao cho x(y+1)-y=6
`x(y+1)-y=6` `=>x(y+1)-(y+1)=6-1` `=>(y+1)(x-1)=5` Vì `x,y in ZZ` `=>x-1,y+1 in ZZ` `=>x-1,y+1 in Ư(5)={+-1,+-5}` TH1: `x-1=1,y+1=5` `=>x=2,y=4(tm)` TH2: `x-1=5,y+1=1` `=>x=6,y=0(tm)` TH3: `x-1=-1,y+1=-5` `=>x=0,y=-6(tm)` TH4: `x-1=-5,y+1=-1` `=>x=-4,y=-2(tm)` Vậy `(x,y) in {(2,4),(6,0),(0,-6),(-4,-2)}` Bình luận
`x(y+1)-y=6`
`=>x(y+1)-(y+1)=6-1`
`=>(y+1)(x-1)=5`
Vì `x,y in ZZ`
`=>x-1,y+1 in ZZ`
`=>x-1,y+1 in Ư(5)={+-1,+-5}`
TH1:
`x-1=1,y+1=5`
`=>x=2,y=4(tm)`
TH2:
`x-1=5,y+1=1`
`=>x=6,y=0(tm)`
TH3:
`x-1=-1,y+1=-5`
`=>x=0,y=-6(tm)`
TH4:
`x-1=-5,y+1=-1`
`=>x=-4,y=-2(tm)`
Vậy `(x,y) in {(2,4),(6,0),(0,-6),(-4,-2)}`