Question

if m-n = 16 and m²-n²=400 find mn

Answer 1

m-n =16 ----(1)

m^2 - n^2 =400

(m+n)(m-n) =400
(m+n)*16 = 400[from (1)]

m+n = 400/16

m+n = 25---(2)

4mn = (m+n)^2  - (m- n )^2
        = (25)^ - (16)^2

4mn = 625 -256

mn = 369/4

Answer 2

m-n=16
m^2-n^2=400
we have m^2-n^2=(m+n)(m-n)
(m+n)(m-n)=400
(m+n)(16)=400
m+n=400/16
m+n=25
that is m=25- n
and n=25-m
mn =(25- n)(25-m)
625-25m-25n+mn