Question

If x : 4, 25. Then show that A.M > G.M > H.M​

Answer 1

SOLUTION

TO PROVE

A.M > G.M > H.M

EVALUATION

Here the given numbers are 4 and 25

So the arithmetic mean

= A.M

$\displaystyle \sf{ = \frac{4 + 25}{2} }$

$\displaystyle \sf{ = \frac{29}{2} }$

$\displaystyle \sf{ = 14.5}$

The geometric mean

= G.M

$\displaystyle \sf{ = \sqrt{4 \times 25} }$

$\displaystyle \sf{ = \sqrt{100} }$

$\displaystyle \sf{ = 10}$

Harmonic mean

= H.M

$\displaystyle \sf{ = \frac{2 \times 4 \times 25}{4 + 25} }$

$\displaystyle \sf{ = \frac{200}{29} }$

$\displaystyle \sf{ = 6.89 }$

∴ A.M > G.M > H.M

Hence proved

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. If the middle term of a finite AP with 7 terms is 21 find the sum of all terms of the AP

https://brainly.in/question/30198388

2. find the 100th term of an AP whose nth term is 3n+1

https://brainly.in/question/22293445

3. 2,7,12,17,..sum of 12 terms of this A. P. is

https://brainly.in/question/24134044

Answer 2

Step-by-step explanation:

1.A.M

2.H.M

3.G.M

Hence the final answer is AM》GM》HM