Question

If m-n=16andm^2+n^2=400,then find mn

Answer 1

Answer:

mn = 72

Step-by-step explanation:

Given---> m - n = 16 and m² + n² = 400

To find ----> Value of mn

Solution---> We have an identity as follows

( a - b )² = a² + b² - 2ab

Putting a = m and b = n in it , we get,

=> ( m - n )² = m² + n² - 2 mn

=> ( m - n )² = ( m² + n² ) - 2mn

Putting m - n = 16 and m² + n² = 400 , we get,

=> ( 16 )² = ( 400 ) - 2 mn

=> 256 = 400 - 2mn

=> 2 mn = 400 - 256

=> 2 mn = 144

=> mn = 144 / 2

=> mn = 72

Addotional identities--->

1) ( a + b )² = a² + b² + 2ab

2) (a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ca

3) a² - b² = ( a + b ) ( a - b )

4) a³ + b³ = ( a + b ) ( a² + b² - ab )

5) a³ - b³ = ( a - b ) ( a² + b² + ab )

6) ( a + b )³ = a³ + b³ + 3ab ( a + b )

7) ( a - b )³ = a³ - b³ - 3ab ( a - b )

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Answer 2

$<font color =“orange”>$

${ \huge \bf{ \mid{ \overline{ \underline{Answer}}} \mid}}$

$\huge\underline{\underline{\texttt{\purple{mn=72}}}}$

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