If (x3 – y3) : (x2 +xy +y2) = 5 : 1and (x2

If (x³ – y³) : (x² +xy +y²) = 5 : 1
and (x² – y²) : (x – y) = 7 : 1, then the ratio 2x : 3y equals

x³ − y³	=	5
x² + xy + y²	=	1

⇒	(x − y)(x² + xy + y²)	= 5
	x² + xy + y²

⇒ x – y = 5 ....(i)
Again,

x² − y²	= 7
x − y

⇒	(x + y)(x − y)	= 7
	x − y

⇒ x + y = 7 ....(ii)
On adding equations (i) and (ii),
2x = 12 ⇒ x = 6
From equation (ii),
x + y = 7 ⇒ y = 7 – 6 = 1

∴	2x	=	2 × 6	= 4 : 1
	3y		3 × 1