Question

X^4-9x^2+20
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X^4-10x^2+24

Answer 1

Ответ:

$\frac{ {x}^{4} - 9 {x}^{2} + 20}{ {x}^{4} - 10 {x}^{2} + 24 } = ...$

$y = {x}^{2}$

$... = \frac{ {y}^{2} - 9y + 20 }{ {y}^{2} - 10y + 24} = ...$

${y}^{2} - 10y + 24 = 0 \\ y1 + y2 = 10 \\ y1y2 = 24 \\ y1 = 6 \\ y2 = 4$

x ≠ ±√6

x ≠ ±2

${y}^{2} - 9 y + 20 = 0 \\ y1 + y2 = 9 \\ y1y2 = 20 \\ y1 = 4 \\ y2 = 5$

x = ±√5

$... = \frac{ (x - \sqrt{5} )(x + \sqrt{5} )(x - 2)(x + 2) }{(x - \sqrt{6})(x + \sqrt{6} )(x - 2)(x + 2) } = \\ = \frac{ {x}^{2} - 5 }{ {x}^{2} - 6 }$