Пошаговое объяснение:
1.
{(x+2)²+y²=10 {(x+2)²+(-(x+4)²=10 {x²+4x+4+x²+8x+16=10
{x+y+4=0 {y=-x-4=-(x+4) {y=-(x+4)
2x²+12x+20=10
2x²+12x+10=0 |÷2
x²+6x+5=0 D=16 √D=4
x₁=-1 y=-(-1+4)=-3 y₁=-3.
x₂=-5 y=-(-5+4)=1 y₂=1.
ответ: x₁=-1 y₁=-3 x₂=-5 y₂=1.
2.
{x-4y=2 {x=4y+2
{xy+2y=8 {(4y+2)*y+2y=8 {4y²+2y+2y=8 4y²+4y-8=0 |÷4
y²+y-2=0 D=9 √D=3
y₁=-2 x=4*(-2)+2=-8+2=-6 x₁=-6
y₂=1 x=4*1+2=4+2=6 x₂=6.
ответ: x₁=-6 y₁=-2 x₂=6 y₂=1.
3.
{(y/x)-(x/y)=16/15 {(y²-x²)/xy=16/15 {15*(y²-x²)=16xy 15y²-15x²=16xy
{4y-5x=15 {4y=5x+15 {y=5*(x+3)/4
15*(5*(x+3)/4)²-15x²=16*x*(5*(x+3))/4)
15*(25*(x+3)²/16-15x²=4*x*5*(x+3)
15*(25*(x+3)²/16-15x²=4*x*5*(x+3)/4 |×16
15*25*(x²+6x+9)-15*16*x²=16*4*5*x*(x+3) |÷5
3*25*(x²+6x+9)-3*16*x²=64*x*(x+3)
75*(x²+6x+9)-48*x²=64x²+192x)
75x²+450x+675-48x²-64x²-192x=0
-37x²+258x+675=0 D=166464 √D=408
x₁=9 y₂=5*(9+3)/4=5*12/4=5*3=15 y₁=15
x₂=-75/37 y₂=5*((-75/37)+3)/4=5*((-75+111)/37)/4=5*36/(37*4)=45/37.
ответ: x₁=9 y₁=15 x₂=-75/37 y₂=45/37.
6*(p+3k-9t)=6p+18k-54t