solvefor m, 3/4 = 1/(n^2)-1/(m^2)

解

解く

m, \frac{3}{4} = \frac{1}{n ^{2}} - \frac{1}{m ^{2}}

m = i \frac{2 n - 4 + 3 n ^{2}}{- 4 + 3 n ^{2}}, m = - i \frac{2 n - 4 + 3 n ^{2}}{- 4 + 3 n ^{2}}; n \neq = \frac{2}{3}, n \neq = - \frac{2}{3}

解答ステップ

\frac{3}{4} = \frac{1}{n ^{2}} - \frac{1}{m ^{2}}

LCMで乗じる

3 m^{2} n^{2} = 4 m^{2} - 4 n^{2}

解く

3 m^{2} n^{2} = 4 m^{2} - 4 n^{2} : m = i \frac{2 n - 4 + 3 n ^{2}}{- 4 + 3 n ^{2}}, m = - i \frac{2 n - 4 + 3 n ^{2}}{- 4 + 3 n ^{2}}; n \neq = \frac{2}{3}, n \neq = - \frac{2}{3}

m = i \frac{2 n - 4 + 3 n ^{2}}{- 4 + 3 n ^{2}}, m = - i \frac{2 n - 4 + 3 n ^{2}}{- 4 + 3 n ^{2}}; n \neq = \frac{2}{3}, n \neq = - \frac{2}{3}