Վարժ․ 284
ա) { x+y=3; xy= -40=> { x=3-y; (3-y)*y= -40=> { x=3-y; 3y-y2= -40=> { x=3-y; -y2+3y+40=0 (1)
-y2+3y+40=0
D=9-(-160)=169
[ y= -3-13/(-2); y= -3+13/(-2)=> [ y= -16/(-2); y=10/(-2)=> [ y=8; y= -5
(1)=> { x=3-y; [ y=8; y= -5=> [{ x=3-y; y=8; { x=3-y; y= -5=> [{ x= -5; y=8; { x=8; y= -5
Պատ՝․ (-5; 8) & (8; -5)
բ) { x+y=7; xy=12=> { x=7-y; (7-y)*y=12=> { x=7-y; 7y-y2=12=> { x=7-y; -y2+7y-12=0 (1)
-y2+7y-12=0
D=49-48=1
[ y= -7-1/(-2); y= -7+1/(-2)=> { y= -8/(-2); y= -6/(-2)=> { y=4; y=3
(1)=> { x=7-y; [ y=4; y=3=> [{ x=7-y; y=4; { x=7-y; y=3=> [{ x=3; y=4; { x=4; y=3
Պատ՝․ (3; 4) & (4; 3)
գ) { x+y=3; xy= -28=> { x=3-y; (3-y)*y= -28=> { x=3-y; -y2+3y+28=0 (1)
-y2+3y+28=0
D=9+112=121
[ y= -3-11/(-2); y= -3+11/(-2)=> [ y= -14/(-2); y=8/(-2)=> [ y=7; y= -4
(1)=> { x=3-y; [ y=7; y= -4=> [{ x= -4; y=7; [ x=7; y= -4
Պատ՝․ (-4; 7) & (7; -4)
դ) { x+y= -8; xy=15=> { x= -8-y; (-8-y)*y=15=> { x= -8-y; -y2-8y-15=0 (1)
-y2-8y-15=0
D=64-60=4
[ y=8-2/(-2); y=8+2/(-2)=> [ y=6/(-2); y=10/(-2)=> [ y= -3; y= -5
(1)=> { x= -8-y; [ y= -3; y= -5=> [{ x= -5; y= -3; { x= -3; y= -5
Պատ՝․ ( -5; -3) & ( -3; -5)
ե) { xy= -15; x-y= -8=> { (-8+y)*y= -15; x= -8+y=> { y2-8y+15=0; x= -8+y (1)
y2-8y+15=0
D=64-60=4
[ y=8-2/2; y=8+2/2=> [ y=6/2; y=10/2=> [ y=3; y=5
(1)=> { x= -8+y; [ y=3; y=5=> [{ y=3; x= -5; { y=5; x= -3
Պատ՝․ ( -5; 3) & ( -3; 5)
զ) { xy=8; x-y=2=> { (2+y)*y=8; x=2+y=> { 2y+y2=8; x=2+y=> { y2+2y-8=0; x=2+y (1)
y2+2y-8=0
D=4-(-32)=36
[ y= -2-6/2; y= -2+6/2=> [ y= -8/2; y=4/2=> [ y= -4; y=2
(1)=> { x=2+y; [ y= -4; y=2=> [{ y= -4; x= -2; { y=2; x=4
Պատ՝․ ( -2; -4) & ( 4; 2)
Վարժ․ 285
ա) { x2+y2=41; y-x=1=> { x2+y2=41; y=1+x=> { x2+(1+x)2=41; y=1+x=> { x2+1+2x+x2-41=0; y=1+x=> { 2x2+2x-40=0; y=1+x (1)
2x2+2x-40=0
D=4+320=324
[ x= -2-18/4; x= -2+18/4=> [ x= -20/4; x=16/4=> [ x= -5; x=4
(1)=> { y=1+x; [ x= -5; x=4=> [{ x= -5; y= -4; { x=4; y=5
Պատ՝․ ( -5; -4) & (4; 5)
բ) { x2+y2=13; y-x=1=> { x2+(1+x)2=13; y=1+x=> { x2+1+2x+x2-13=0; y=1+x=> { 2x2+2x-12=0; y=1+x (1)
2x2+2x-12=0
D=4-(-96)=100
[ x= -2-10/4; x= -2+10/4=> [ x= -12/4; x=8/4=> [ x= -3; x=2
(1)=> { y=1+x; [ x= -3; x=2=> [{ y= -2; x= -3; { y=3; x=2
Պատ՝․ ( -3; -2) & (2; 3)
գ) { x2-y2=3; x+y=1=> { (1-y)2-y2=3; x=1-y=> { 1-2y+y2-y2-3=0; x=1-y=> { -2y-2=0; x=1-y=> { y= -1; x=2
Պատ՝․ (2; -1)
դ) { x-y=2; x2-y2=8=> { x=2+y; (2+y)2-y2=8=> { x=2+y; 4+4y+y2-y2-8=0=> { x=2+y; 4y-4=0=> { x=3; y=1
Պատ՝․ (3; 1)
ե) { x+y= -6; y2-x2=3=> { x= -6-y; y2-(-6-y)2=3=> { x= -6-y; y2-36-12y-y2=3=> { x= -6-y; -12y-39=0=> { x= -11/4; y= -13/4
Պատ՝․ ( -11/4; -13/4)
զ) { x-y= -3; y2-x2= -1=> { x= -3+y=y-3; y2-(-3+y)2= -1=> { x=y-3; y2-y2+9y-9+1=0=> { x=y-3; 9y-8=0=> { x= -1/9; y=8/9
Պատ՝․ ( -1/9; 8/9)
Վարժ․ 286
ա) { x2-y2=0; y+x=0=> { x2-y2=0; y= -x=> { x2-(-x)2=0; y= -x=> { x2-x2=0; y= -x=> { 0=0; y= -x
Պատ՝․ (x; -x)
բ) x2-y2=0; y-x=0=> { x2-y2=0; y=x=> { x2-(x)2=0; y=x=> { x2-x2=0; y=x=> { 0=0; y=x
Պատ՝․ (x; x)
գ) { x+y=0.2; x2-y2=2=> { x= -y+0.2; x2-y2=2=> { x= -y+0.2; (-y+0.2)2-y2=2=> { x= -y+0.2; y2-0.4y+0.04-y2-2=0=> { x= -y+0.2; -0.4y-1.96=0=> { y= -0.49; x= -y+0.2=> 0.49+2=2.49
Պատ՝․ (2.49; -0.49)
դ) { x-y=0.6; y2-x2=12=> { x=0.6+y; y2-(0.6+y)2=12=> { x=0.6+y; y2-0.36-1.2y-y2-12=0=> { x=0.6+y; -1.2y-12.36=0=> { x=0.6+y; -1.2y=12.36=> { x=0.6+y; y= -10.3=> { x= -9.7; y= -10.3
Պատ՝․ ( -9.7; -10.3)
ե) { x-y=11; xy=12=> { x=11+y; (11+y)*y=12=> { x=11+y; 11y+y2-12=0=> { x=11+y; y2+11y-12=0 (1)
y2+11y-12=0
D=121+48=169
[ y= -11-13/2; y= -11+13/2=> [ y= -24/2; y=2/2=> [ y= -12; y=1
(1)=> { x=11+y; [ y= -12; y=1=> [{ x= -1; y= -12; { x=12; y=1
Պատ՝․ ( -1; -12) & (12; 1)
զ) [ y-x=4; xy=5=> { y=4+x; x*(4+x)=5=> { y=4+x; 4x+x2-5=0=> { y=4+x; x2+4x-5=0 (1)
x2+4x-5=0
D=16+20=36
[ x= -4-6/2; x= -4+6/2=> { x= -10/2; x= 2/2=> { y= -5; y=1
(1)=> { y=4+x; [ y= -5; y=1=> [{ y= -1; x= -5; { y=5; x=1
Պատ՝․ (-5; -1) & (1; 5)
է) { xy=12; y+x=1=> { x*(1-x)=12; y=1-x=> { x-x2-12=0; y=1-x=> { -x2+x-12=0; y=1+x (1)
D=1-48= -47 (Ø)
Պատ՝․ Ø
ը) { xy=15; x+y= -5=> { (-5-y)*y=15; x= -5-y=> { -5y-y2-15=0; x= -5-y=> { -y2-5y-15=0; x= -5-y (1)
D=25-60= -35 (Ø)
Պատ՝․ Ø
թ) { x-y=2; xy= -13=> { x=2+y; (2+y)*y= -13=> { x=2+y; 2y+y2+13=0=> { x=2+y; y2+2y+13=0 (1)
D=4-52= -48 (Ø)
Պատ՝․ Ø
Վարժ․ 289
ա) { x+y+z=6; y+z=3; z=1=> { x+y+z=6; y=2; z=1=> { x=6-3; y=2; z=1=> { x=3; y=2; z=1
Պատ՝․ (3; 2; 1)
բ) { x+y+z=0; x+z=2; x= -1=> { x+y+z=0; z=3; x= -1=> { -1+y+3=0; z=3; x= -1=> { y= -2; z=3; x= -1
Պատ՝․ ( -1; -2; 3)
գ) { x+y+z=2; x+z=1; x+y=3=> { 1-z+y+z=2; x=1-z; 1-z+y=3=> { 1+y=2; x=1-z; 1-z+y=3=> { y=1; x=1-z; 1-z+1=3=> { y=1; x=2; z= -1
Պատ՝․ (2; 1; -1)
դ) { x+y+z=2; y+z=3; x+y=1=> { x+3-z+z=2; y=3-z; x+3-z=1=> { x+3=2; y=3-z; x+3-z=1=> { x= -1; y=2; z=1
Պատ՝․ (-1; 2; 1)
ե) { x+y+z= -1; x+2y= -1; x-y=5=> { 5+y+y+z= -1; 5+y+2y= -1; x=5+y=> { 5+2y+z= -1; 5+3y+1=0; x=5+y=> { 5+2y+z= -1; 6+3y=0; x=5+y=> { 5+2y+z= -1; y= -2; x=3=> { 5+(-4)+z+1=0; y= -2; x=5+(-2)=> { z= -2; y= -2; x=3
Պատ՝․ (3; -2; -2)
զ) { x+y+z= -1; 2y+z=4; y-z=5=> { x+5+z+z= -1; 10+2z+z=4; y=5+z=> { x+5+2z= -1; 10+3z-4=0; y=5+z=> { x+5+2z= -1; 6+3z=0; y=5+z=> { x+5+2z= -1; z= -2; y=3=> { x+5+(-4)+1=0; z= -2; y=3=> { x= -2; z= -2; y=3
Պատ՝․ (-2; 3; -2)
է) { x+y+z= -1; x-y+z=7; x+y= -3=> { -3-y+y+z= -1; -3-y-y+z=7; x= -3-y=> { -3+z= -1; -3-2y+z=7; x= -3-y=> { z=2; -3-2y+z-7=0; x= -3-y=> { z=2; -2y= -8=> y=4; x= -7=> { z=2; y=4; x= -7
Պատ՝․ (-7; 4; 2)
ը) { x+y+z=1; x+y-z= -3; y+z=4=> { x+4-z+z=1; x+4-z-z= -3; y=4-z=> { x+4=1; x+4-2z= -3; y=4-z=> { x= -3; x+4-2z+3=0; y=4-z=> { x= -3; -3+4-2z+3=0; y=4-z=> { x= -3; z=2; y=2
Պատ՝․ ( -3; 2; 2)
թ) { x+y+z=3; x+2y+3z=6; 2x-y+z=2=> { x+y+z=3; 2x-y+z=2; { x+2y+3z=6; 2x-y+z=2=> { 3x+2z=5; 5x+5z=10=> { z=1; x=1=> y=1
Պատ՝․ (1; 1; 1)
ժ) { x+y+z= -3; x-y+z= -1; x+2y-z= -2=> { x+y+z= -3; x+2y-z= -2; { x-y+z= -1; x+2y-z= -2=> { 2x+2z= -2; 3x+z= -4=> { z= -1; x= -1=> y= -1
Պատ՝․ (-1; -1; -1)
Դավիթ Մուրադյան 