(5x^2+1)/((x^2)-5(x+1/x)+8)=0

解

\frac{5 x ^{2} + 1}{( x ^{2} ) - 5 ( x + \frac{1}{x} ) + 8} = 0

x = \frac{1}{5} i, x = - \frac{1}{5} i

解答ステップ

\frac{5 x ^{2} + 1}{( x ^{2} ) - 5 ( x + \frac{1}{x} ) + 8} = 0

簡素化

\frac{5 x ^{2} + 1}{( x ^{2} ) - 5 ( x + \frac{1}{x} ) + 8} : \frac{5 x ^{2} + 1}{x ^{2} - 5 ( x + \frac{1}{x} ) + 8}

\frac{5 x ^{2} + 1}{x ^{2} - 5 ( x + \frac{1}{x} ) + 8} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

5 x^{2} + 1 = 0

解く

5 x^{2} + 1 = 0 : x = \frac{1}{5} i, x = - \frac{1}{5} i

x = \frac{1}{5} i, x = - \frac{1}{5} i