Question

if m is the arithmetic mean g is the geometric mean and h is the harmonic mean of positive numbers a and b which of the following is false​

Answer 1

Answer:

If A is an arithmetic mean between a and b then A=

2

a+b

.

If G is an geometric mean between a and b then G=

ab

.

If H is an harmonic mean between a and b then H=

a+b

2ab

.

Now consider AH

AH=(

2

a+b

)(

a+b

2ab

)

AH=ab

AH=G

2

Since AH=G

2

, therefore, A, G and H are in G.P.

Hence option A is correct.

Answer 2

Answer:

if a is an arithmetic mean between a and b then A equals a plus b / 2

if G is an geometric mean between a and b then G equals ab.

if H is an hormonic mean between a and b then H equals 2ab / a plus b .