Question

розв'язати рівняння​

Answer 1

$\frac{(x - 5)(x - 6)(x - 7)}{ {x}^{2} - 7x + 10 }$

(х-5)(х-6)(х-7) = 0

х²-7х+10 ≠ 0 => (х-5)(х-2)≠0

х = 5

х = 6

х = 7

х ≠ 5

х ≠ 2

Ответ: х = 6, х = 7

$( {x}^{2} \frac{4}{ {x}^{2} } ) - (x + \frac{2}{x} )- 8 = 0 \\ 4 - x - \frac{2}{x} - 8 = 0 \\ x + \frac{2}{x} + 4 = 0 \\ {x}^{2} + 4x + 2 = 0 \\ x1 = - 2 + \sqrt{2} \\ x2 = - 2 - \sqrt{2}$

Ответ : -2 ± √2

$( {x}^{2} + \frac{1}{ {x}^{2} } ) + 7(x - \frac{1}{x} ) + 1 = 0$

Пусть х-1/х= t, тогда х²+1/х²= t² + 2

${t}^{2} + 2 + 7t + 10 = 0 \\ {t}^{2} + 7t + 12= 0 \\ t1 = - 3 \\ t2 = - 4$

Обратная замена :

$x - \frac{1}{x} = - 3 \\ {x}^{2} - 1 = - 3x \\ {x}^{2} + 3x - 1 = 0 \\ x1 = \frac{ - 3 - \sqrt{13} }{2} \\ x2 = \frac{ - 3 + \sqrt{13} }{2}$

$x - \frac{1}{x} = - 4 \\ {x}^{2} - 1 = - 4x \\ {x}^{2} + 4x - 1 = 0 \\ x3 = - 2 + \sqrt{5} \\ x4 = - 2 - \sqrt{5}$

Ответ : (-3±√13)/2 , -2±√5