Question

ecuacion lineal (x+1+6/x)(x-1+6/×)=24

Answer 1

Explicación paso a paso:

$( \frac{x + 1 + 6}{x} )( \frac{x - 1 + 6}{x} ) = 24 \\ ( \frac{x + 7}{x} )( \frac{x + 5}{x} ) = 24 \\ (1 + \frac{7}{x} )(1 + \frac{5}{x} ) = 24 \\ 1 + \frac{5}{x} + \frac{7}{x} + \frac{35}{ {x}^{2} } = 24 \\ 1 + \frac{12}{x} + \frac{35}{ {x}^{2} } = 24\\ \frac{ {x}^{2}(1) + x(12) + 35}{ {x}^{2} } = 24 \\ \frac{ {x}^{2} + 12x + 35 }{ {x}^{2} } = 24 \\ {x}^{2} + 12x + 35 = 24 {x}^{2} \\ {x}^{2} + 12x - 24 {x}^{2} + 35 = 0 \\ - 23 {x}^{2} + 12x + 35 = 0 \\ por \: ecuación \: general \: \\ a = - 23 \: \: \: b = 12 \: \: \: c = 35 \\ x = \frac{ - b \binom{ + }{ - } \sqrt{( {b})^{2} - 4ac } }{2a} \\ x = \frac{ - 12 \binom{ + }{ - } \sqrt{( {12})^{2} - 4( -23)(35) } }{2( - 23)} \\ x = \frac{ - 12 \binom{ + }{ - } \sqrt{144 + 3220} }{ - 46} \\ x = \frac{ - 12 \binom{ + }{ - } \sqrt{3364} }{ - 46} \\ x = \frac{ - 12 \binom{ + }{ - } 58}{ - 46} \\ x = \frac{ - 12 + 58}{ - 46} = \frac{46}{ - 46} = - 1 \\x = \frac{ - 12 - 58}{ - 46} = \frac{ - 70}{ - 46} = 1 \frac{12}{23} \\ \\ x = - 1 \\ x = 1 \frac{12}{23}$