Question

X^4-17x^2+16=0
Помогите пж

Answer 1

x⁴ - 17x² + 16 = 0
Сделаем замену x² = m ≥ 0
m² - 17m + 16 = 0
D = (- 17)² - 4 * 1 * 16 = 289 - 64 = 225 = 15²
$m_{1}= \frac{17+15}{2}=16\\\\ m_{2}= \frac{17-15}{2} =1\\\\ x^{2} =16\\\\ x_{1}= \sqrt{16}=4\\\\ x_{2} =- \sqrt{16}=-4 \\\\\\ x^{2} =1\\\\ x_{3} = \sqrt{1}=1\\\\ x_{4} =- \sqrt{1} =-1$
Ответ: - 4 ; - 1 ; 1 ; 4