Question

2x² + 3y² Alpha xy then prove that X Alpha y​

Answer 1

Answer:

this is homogeneous equation. let's try to break in simpler form.

2x² + 3xy - y² = 0

dividing by y² from both sides,

⇒2x²/y² + 3xy/y² - y²/y² = 0

⇒2(x/y)² + 3(x/y) - 1 = 0

let (x/y) = m

then , 2m² + 3m - 1 = 0 now it is in the form of quadratic equation.

using formula, a = {-b ± √(b² - 4ac)}/2a

m = {-3 ± √(3² + 8)}/2(2)

= {-3 ± √17}/4

so, m = (-3 + √17)/4 , (-3 - √17)/4

or, y/x = (-3 + √17)/4, (-3, -√17)/4

or, y = {(-3 + √17)/4} x , {(-3 -√17)/4}x

hence, it is clear that, y ∝ x or, x ∝ y

Step-by-step explanation: