, , . .
III . . "" . 189 . , .. .
( ). : .
1.15. ( "" ). , .
. . . ,
x 2+2 x +1=(x +1)2.
, 2.
2 + 1. x 2−2 x +1=(x −1)2.
, 4 , 2 - 4 . , , 6 + 1, , 112 = 121.
6 + 1 = 121,
= 20. : 80, 320, 41. , , , , 6 + 1 = 132 6 + 1 = 52.
, , . , . . □
. 80, 320, 41.
1.16. , 30 , 2, 3, 4, 5. 93, "" , "", , "". , "" 10, '" . ?
. "" , "" , "" z, "" u. :
x + y + z + u =30,2 x + 3 y + 4 z + 5 u = 93,
y > u,
y < z,
z = k ⋅10,
u =2 l,
l, k .
,
1 2
x +2 y +3 z +4 u =63. | (8) |
|
|
z 10, k 1. , k > 1 (8) . , z = 10.
, (8) x +2 y +4 u =33.
u ( < 10) u = 2,4,6,8. u = 6 u= 8 , u > . , 4 2.
u = 4 :
x +2 y =17,2 x + 3 y = 33,
= 1, = 15,
> u. u = 2
x + 2 y = 25, .
2 x + 3 y = 43
= 11, = 7 . □ . "" 2, "" 10, "" 7, "" 11. 1.17.
, , 15/19 . 3/7 2/5 , 1000 , 1000 . ?
. , , :
x =1915 y,74 x <1000,
53 y >1000.
, 5 19, , .. 95. 7 15, .. 105.
y = 95 y 1, x =105 x 1.
:
7 x 1 = 5 y 1,
3 x 1 < 50,
57 y 1 >1000,
1 1 .
, ( ) 1 5, a 1 7, x 1 = 5 x 2, y 1 = 7 y 2.
x 2= y 2, x 2<4, y 2>2.
, 2 = y 2 = 3. x =7⋅15 x 1⋅5 x 2=1575,
y =5⋅19 y 1=5⋅19⋅7 y 2=1995.□. 1575 1995.