UPSEE Solved Model Paper 2

AM =

a+b

2

GM = √ab
Given, AM = 3GM
∴

a+b

2

= 3√ab
Squaring both sides, we get
⇒ a2+b2 + 2ab = 36ab
⇒ a2+b2 - 34ab = 0
⇒ (

a

b

)2−34(

a

b

) + 1 = 0
⇒ (

a

b

) =

34±√1152

2

= 17 ± √288
From option (2):
3+√8:3−√8 is equal to

3+√8

3−√8

×

3+√8

3+√8

= 17 + √288