Question

answer this question of ratio and proportions

Answer 1

$using \: componendo \: and \: dividendo \\ \frac{ {x}^{2} - x + 1 + {x}^{2} + x + 1}{ {x}^{2} - x + 1 - {x}^{2} - x - 1 } = \frac{14x - 14 + 13 x + 13}{14x - 14 - 13x - 13} \\ \frac{2 {x}^{2} + 2 }{ - 2x} = \frac{27x - 1}{x - 27} \\ \frac{ {x}^{2} + 1}{ - x} = \frac{27x - 1}{x - 27} \\ ( {x}^{2} + 1)(x - 27) = - x(27x - 1) \\ {x}^{3} + x - 27 {x}^{2} - 27 = - 27 {x}^{2} + x \\ {x}^{3} - 27 = 0 \\ {x}^{3} = 27 \\ x = 3$