Question

$x^{4} -2x^{2} -15=0$

Товаарищи помогите решить)

Answer 1

Ответ:

${x}^{2} = y \\ {y}^{2} - 2y - 15 = 0 \\ d = {( - 2)}^{2} - 4 \times 1 \times ( - 15) = 4 + 60 = 64 \\ y1 = \frac{ - b + \sqrt{d} }{2a} = \frac{ - ( - 2) + \sqrt{64} }{2 \times 1} = \frac{2 + 8}{2} = \frac{10}{2} = 5$

$y2 = \frac{ - b - \sqrt{d} }{2a} = \frac{ - ( -2) - \sqrt{64} }{2 \times 1} = \frac{2 - 8}{2} = \frac{ - 6}{2} = - 3$

${x}^{2} = y \\ {x}^{2} = 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {x }^{2} = - 3 \\ x 1 = \sqrt{5} \\ x2 = - \sqrt{5}$