bai 17
a)
x^2+y^2+2x+4y+5=0
<=>(x+1)^2+(y+2)^2=0
(x,y)=(-1,-2)

c) 2x^2-8x+y^2+2y+9=0
<=>2(x-2)^2+(y+1)^2=0
(x,y)=(2,-1)

Bài 16

bài 18

Bài 17
a) x^2 + y^2 - 2x + 4y + 5 = 0.
<=> x^2 - 2x + 1 + y^2 + 4y + 4 = 0
<=> (x - 1)^2 + (y - 2)^2 = 0
<=> {x - 1 = 0. <=>{x = 1
        {y - 2 = 0        {y = 2

Bài 18
a)(a+b+c)^2+a^2+b^2+c^2
=a^2+b^2+c^2 +2ab+2bc+2ac+a^2+b^2+c^2
=a^2+2ab+b^2+b^2+2bc+c^2+a^2+2ac+c^2
=(a+b)^2+(b+c)^2+(a+c)^2

b)
2(a-b)(c-b)+2(b-a)(c-a)+2(b-c)(a-c)
=2(ac-ab-bc+b^2)+2(bc-ab-ac+a^2)+2(ab-bc-ac+c^2)
=2ac-2ab-2bc+2b^2+2bc-2ab-2ac+2a^2+2ab-2bc-2ac+2c^2
=2a^2+2b^2+2c^2-2ac-2bc-2ac
=a^2-2ac+c^2+b^2-2bc+c^2+a^2-2ab+b^2
=(a-c)^2+(b-c)^2+(a-b)^2

Bài 17b

Bài 17c
2x^2-8x+y^2+2y+9=0
(2x^2-8x+8)+(y^2+2y+1)=0
2(x^2-4x+4)+(y+1)^2=0
2(x-2)^2+(y+1)^2=0
=> x-2=0 => x=2
y+1=0 => y=-1

bai 18
a/
A=(a+b+c)^2+a^2+b^2+c^2
A=a^2+b^2+c^2+2ab+2ac+2bc+a^2+b^2+c^2
A=(a^2+2ab+b^2)+(a^2+2ac+c^2)+(b^2+2bc+c^2)
A=(a+b)^2+(b+c)^2+(c+a)^2

b/
B=2(a-b)(c-b)+2(b-a)(c-a)+2(b-c)(a-c)
a-b=x; b-c=y; c-a=z
(x+y+z=0)(*)
B=-2xy-2xz--2yz
-B=(xy+xz)+(xy+yz)+(xz+yz)
=x(y+z)+y(x+z)+z(x+y
(*)<=>-x^2-y^2-z^2
B=(a-b)^2+(b-c)^2+(c-a)^2