Question

Решите биквадратное уравнение x⁴-8x²-9=0

Answer 1

$x {}^{4} - 8x {}^{2} - 9 = 0 \\ x {}^{2} = y \\ y {}^{2} - 8y - 9 = 0 \\ d = 64 + 36 = 100 \\ y = \frac{8 + 10}{2} = \frac{18}{2} = 9 \\ y = \frac{8 - 10}{2} = \frac{ - 2}{2} = - 1 \\ x {}^{2} = 9 \\ x = 3 \\ x = - 3 \\ {x}^{2} = - 1$

Answer 2

X^4-8x^2-9=0
x^2=t>0
t^2-8t-9=0
D=16+9=25>0
t1=4+√25=4+5=9
t2=4-5=-1
x^2=9
x= 3 ;x=-3