Question

find the value of = mn if m+n=8 and m-n=2 [ans=15]​

Answer 1

Answer:

m+n = 8

5+3 = 8

m-n =2

5-3 = 2

m = 5 , n= 3

Answer 2

$\begin{gathered}\begin{gathered}\bf Given -  \begin{cases} &\sf{m \: + \: n \: = 8} \\ &\sf{m \: - \: n \: = 2} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf  To \:  Find :-  \begin{cases} &\sf{mn}  \end{cases}\end{gathered}\end{gathered}$

$\large\underline\purple{\bold{Solution :- }}$

Given that

$\tt \:  \longrightarrow \: m \: + \: n \: = \: 8 \\ \tt \:  \longrightarrow \: m \: - \: n \: = \: 2$

We know that,

$\tt \:  \longrightarrow \: {(m + n)}^{2} - {(m - n)}^{2} = 4mn$

$\tt\implies \: {(8)}^{2} - {(2)}^{2} = 4mn$

$\tt\implies \:64 \: - \: 4 \: = \: 4mn$

$\tt\implies \:4mn \: = \: 60$

$\tt\implies \:mn \: = \: 15$