Question

If the arithmetic mean of two positive numbers x and y
(x > y) is twice their Geometric mean, then x:y is
(a) 5 + 17:5-7 (b) 2 + V3 : 2 - 3
(c) 5 : 77
(d) 2 : 3​

Answer 1

Answer:

ArithmeticMeanofxandy=

2

x+y

GeometricMeanofxandy=

xy

2

x+y

=2

xy

=>(x+y)

2

=16xy

=>(x−y)

2

=12xy

=>x

2

−14xy+y

2

=0

x=

2

14y±

192y

2

=>x=7y±4

3

y

x=(7+4

3

)y(∵x>y)

∴x:y=(7+4

3

):1