Question

find the arithmetic mean of (m+n)² and (m-n)²​

Answer 1

Answer:

AM IS m²+n²

Step-by-step explanation:

a= (m+n)² and b=(m-n)²​

by using the formula  a+b/2 =AM

(m+n)² +(m-n)²​/2

m²+n²+2mn +m²+n²-2mn/2

(2mn-2mn)=0

m²+n²+m²+n²/2

2m²+2n²/2

taking 2 common

2(m²+n²)/2

2 and 2 cancel out

we have arithmetic mean as  "m²+n²"

hope it helped u !!!

happy new year :)

Answer 2

Question :-

• Find the arithmetic mean of (m+n)² and (m-n)²

Answer :-

Given :-

• Two numbers (m+n)² and (m-n)².

To find :-

• Arithmetic Mean

Formula used :-

$\bf \:Mean = \dfrac{Sum \: of \: observations}{Number \: of \: observations }$

Solution :-

Numbers are (m+n)² and (m-n)²

So, sum of observations = (m+n)² + (m-n)²

= m² + n² + 2mn + m² + n² - 2mn

= 2m² + 2n²

= 2(m² + n²)

Number of observations = 2

$\bf \:Mean = \dfrac{Sum \: of \: observations}{Number \: of \: observations }$

$\bf\implies \:Mean = \dfrac{2( {m}^{2} + {n}^{2} )}{2}$

$\bf\implies \:Mean = {m}^{2} + {n}^{2}$