Question

x2 – 3xy + 2y2 + 3x – 6y + 8 = 0.​

Answer 1

Answer:

(y-x-6)(y-x/2+9)

Step-by-step explanation:

x2 – 3xy + 2y2 + 3x – 6y + 8 = 0.​

dividing by 2

x²/2+y²-3xy/2+3x/2-3y+4=0

Let us take

y= m1x+c1

y=m2x+c2

=(y-m1x-c1)(y-m2x-c2)

= m1m2x²-xy(m1+m2)+x(m1c1²+m2c2)+y(C1+c2)+c1C2= 0

m1m2= 1/2

m1+m2= 3/2

m1c1+m2c2= -3

C1+c2= -3

let m1= 1

m2 = 1/2

then,

m1c1+m2c2= 3/2

1×c1+1×c2/2= 3

C1+c2= -3

equating both

we get,

C2= -9

C1= 6

Answer is

(y-x-6)(y-x/2+9)= 0