Assume that m n 0 then mn n2 mn m2 n2 m2 mn m n mn

Assume that m > n > 0; then mn > n^2 mn - m^2 > n^2 - m^2 m(n - m) > (n + m)(n - m) m > n + m 0 > n But it was assumed that n > 0. Find the error.

Solution

mn > n^2

mn- m^2 > n^2 - m^2

m ( n-m) > (n+m)(n-m )

m > n+m ------- error in this line

since we have assumed earlier that

m > n > 0

so m cannot be greater than n+m