Question

if $5x^2-13xy+6y^2=0$, find x : y

• A. 2 :1 only
• B. 5 : 3 or 1 : 2
• C. 3 : 5 only
• D. 3 : 5 or 2 : 1

Answer 1

Answer:

D. 3 : 5 or 2 : 1

We'll simplify $5x ^ 2 - 13xy + 6y ^ 2 = 0$ by splitting the xy term

$\Rightarrow 5x ^ 2 - 10xy - 3xy + 6y ^ 2 = 0$

5x(x - 2y) - 3y(x - 2y) = 0

(5x - 3y)(x - 2y) = 0

Taking,

5x - 3y = 0 , 5x=3y

x : y = 3 : 5

Taking,

x - 2y = 0 , x = 2y

x : y = 2 : 1

x : y is (3 : 5) or (2 : 1)