Question

m-n=16 and m2+n2=400, then find me

Answer 1

${(m - n)}^{2} = {m}^{2} + {n}^{2} - 2mn \\ {16}^{2} = 400 - 2mn \\ 2mn = 144 \\ mn = 72 \\ m = \frac{72}{n} ..........(1) \\ now \: using \: (1)...... \\ m - n = 16 \\ \frac{72}{n} - n = 16 \\ \frac{72 - {n}^{2} }{n} = 16 \\ {n}^{2} + 16n - 72 = 0 \\ {n}^{2} + 18n - 4n - 72 = 0 \\ n(n + 16) - 4(n + 16) = 0 \\ (n - 4)(n + 16) = 0 \\ hence \: n = 4 \: or - 16 \: .......(2) \\ m - n = 16 \\ m = 16 + n \\ m = 16 + 4 \: or \: m = 16 - 16 \: (from \: (2)) \\ m = 18 \: or \: 0$