Question

2x2+3xy+y2=0 find ratio X:y

Answer 1

2x² + 3xy + y² = 0
dividing both sides, with y²
2x²/y² + 3xy/y² + y²/y² = 0/y²
2(x/y)² + 3(x/y) + 1 = 0
Let (x/y) = P

2P² + 3P + 1 = 0
2P² + 2P + P + 1 = 0
2P( P + 1) + 1(P + 1) = 0
(2P + 1)(P + 1) = 0
P = -1 , -1/2

hence,
(x/y) = -1 or -1/2

Answer 2

Heya User,

--> 2x² + 3xy + y² = 0
=> [ 2x² + 2xy ] + [ xy + y² ] = 0
=> [ 2x + y ][ x + y ] = 0
=> x = -y/2 ; -y
=> x/y = -1/2 ; -1

Hence, x:y = -2 : 1 or -1 : 1