Question

If(4x2 + xy) : (3xy - y2) =12:5 , find (x+2y) : (2x + y).

x2 - square of x
y2 - square of y

Answer 1

(4x^2+xy)/(3xy-y^2)=12/5.

20x^2+5xy=36xy-12y^2.

20x^2–31xy+12y^2=0 , divide both side by x.y

20x/y-31+12.y/x=0 . let x/y=p.

20p-31+12/p=0.

or 20p^2–31p+12=0.

or 20p^2–16p-15p+12=0.

or 4p(5p-4) - 3(5p-4)=0.

or (5p -4) (4p-3)=0.

Either 5p-4=0 =>p=4/5 or x : y = 4 : 5 .

Or 4p-3=0 => p=3/4 or x : y = 3 : 4