Question

If 5x² - 13xy + 6y² = 0 find x : y ?

Answer 1

Answer:

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

Step-by-step explanation:

Given :-

5x² - 13xy + 6y² = 0

To find :-

x : y

Solution :-

Factorization:

• 5x² - 13xy + 6y² = 0

10 × 3 = 30 & 10 - 3 = -13

• 5x² - 10xy - 3xy + 6y² = 0
• 5x(x - 2y) - 3y(x - 2y) = 0
• (x - 2y) (5x - 3y) = 0
• x - 2y = 0 or 5x - 3y = 0
• x = 2y or 5x = 3y
• x/y = 2/1 or x/y = 3/5

∴ (x : y) = (2 : 1) or (3 : 5)

Answer 2

5x

2

−13xy+6y

2

=5x

2

−10xy−3xy+6y

2

=5x(x−2y)−3y(x−2y)

=(5x−3y)(x−2y)

x:y=3:5

         =2:1