CGPET 2021 Solved Paper

Let a and b are two numbers.
Given, G1 and G2 are two geometric mean between a and b.
∴ a,G1,G2,b are in GP.
∵ tn=arn−1 (nth term or GP)
b=a.r4−1⇒r=(

b

a

)

1

3

G1=ar=a×(

b

a

)

1

3

=a

2

3

b

1

3

G2=ar2=a(

b

a

)

2

3

=a

1

3

b

2

3

∴ A be the arithmetic mean of a and b.
⇒ A=

a+b

2

Now, the value

G12

G2

+

G22

G1

=

a 4 3 .b 2 3

a 1 3 b 2 3

+

a 2 3 .b 4 3

a 2 3 b 1 3

=a+b=2A