Question

If (4x(square)+xy): (3xy-ysquare) =12:5 find x+2y:2x+y

Answer 1

(4x² + xy): (3xy - y²) = 12:5

So, we can write as :

→ 4x² + xy/3xy - y² = 12/5

By doing cross multiplication we get,

5(4x² + xy) = 12(3xy - y²)

20x² + 5xy = 36xy - 12y²

20x² + 5xy-36xy + 12y² = 0

→ 20x² - 31xy + 12y² = 0

By doing middle term break we get,

20x² - (16+15)xy + 12y² = 0

→ 20x² - 16xy - 15xy + 12y² = 0

4x(5x - 4y) - 3y(5x - 4y) = 0

(4x - 3y)(5x - 4y) = 0

→ 4x - 3y = 0

→ 4x = 3y

x = 3y/4

And,

5x - 4y = 0

5x = 4y

➡x = 4y/5

Now,

Now,In case I :

⇒ x = 3y/4

Then,

→(x + 2y): (2x + y)

→ x + 2y/2x+y

{3y/4 + 2y)/(2(3y/4) + y}

(3y + 8y)/4 / (6y/4 + y)

11y/4 / 6y + 4y/4

11y/4/ 10y/4c

11/10

In case II:

⇒ x = 4y/5

Then,

→ (x + 2y): (2x + y)

→ x + 2y/2x + y

{4y/5 + 2y)/(2(4y/5) + y}

(4y + 10y)/5/ (8y/5 + y)

14y/5/8y + 5y/5

14/13

:-)The value of (x + 2y): (2x + y) is 11/10

and 14/13.