If (a + b) : √ab = 4 : 1, where a > b

1. (2 + √3) : (2 − √3)
2. (2 − √3) : (2 + √3)
3. (3 + √2) : (3 − √2)
4. (3 − √2) : (3 + √2)

a + b	=	4	⇒	a + b	=	2
√ab	=	1	⇒	2√ab	=	1

By componendo and dividendo,

a + b + 2 √ab	=	3
a + b − 2 √ab	=	1

⇒	(√a + √b)²	=	(√3)²
	(√a − √b)²		(1)²

Again using componendo and dividendo,

2√a	=	√3 + 1
2√b	=	√ 3 − 1

⇒	√a	=	√3 + 1
	√b		√ 3 − 1

On squaring both sides

a	=		√3 + 1		²	=	3 + 1 + 2 √3
b			√ 3 − 1				3 + 1 − 2 √3

=	4 + 2√3	=	2 + √3
	4 − 2√3		2 − √3

2 + √3 : 2 − √3