[tex]\bf{ \frac{x}{1} + \frac{1}{x} = \frac{82}{9} } \\ \\ \bf{\frac{ {x}^{2} + 1}{x } = \frac{82}{9} } \\ \\ \bf{9( {x}^{2} + 1) = 82x } \\ \\ \bf{9 {x}^{2} + 9 = 82x} \\ \\ \bf{ {9x}^{2} - 82x + 9 = 0} \\ \\ \bf{(9x - 1)(x - 9) = 0} \\ \\ \bf{9x - 1 = 0} \\ \\ \bf{9x = 1} \\ \\ \boxed{\bf\red{x = \frac{1}{9} }} \\ \\ \bf{x - 9 = 0 }\\ \\ \boxed{\bf\red{x = 9}}[/tex]
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Determine el número que sumado a su inverso de por resultado
[tex]\bf{ \frac{x}{1} + \frac{1}{x} = \frac{82}{9} } \\ \\ \bf{\frac{ {x}^{2} + 1}{x } = \frac{82}{9} } \\ \\ \bf{9( {x}^{2} + 1) = 82x } \\ \\ \bf{9 {x}^{2} + 9 = 82x} \\ \\ \bf{ {9x}^{2} - 82x + 9 = 0} \\ \\ \bf{(9x - 1)(x - 9) = 0} \\ \\ \bf{9x - 1 = 0} \\ \\ \bf{9x = 1} \\ \\ \boxed{\bf\red{x = \frac{1}{9} }} \\ \\ \bf{x - 9 = 0 }\\ \\ \boxed{\bf\red{x = 9}}[/tex]