Question

Биквадратные уравнения

1) х4 – 10х2 + 1=0

2) х4 + 4х решить!

Answer 1

1)

x1 = $-\sqrt{5-2\sqrt{6} }$

x2 = $\sqrt{5-2\sqrt{6} }$

x3 = $-\sqrt{5+2\sqrt{6} }$

x4 = $\sqrt{5+2\sqrt{6} }$

2)

x1,2 = ±$\sqrt{3}$

Объяснение:

1) х² = у

у² -10у +1 = 0

D = 100 - 4 = 96

y1 = (10 - $4\sqrt{6}$)/2 = 5 - $2\sqrt{6}$ > 0

y2 = (10 + $4\sqrt{6}$)/2  = 5 + $2\sqrt{6}$ > 0

y1 = 5 - $2\sqrt{6}$

x1 = $-\sqrt{5-2\sqrt{6} }$

x2 = $\sqrt{5-2\sqrt{6} }$

y2 = 5 + $2\sqrt{6}$

x3 = $-\sqrt{5+2\sqrt{6} }$

x4 = $\sqrt{5+2\sqrt{6} }$

2) х² = у

у² + 4у - 21 = 0

D = 16 + 84 = 100 = 10²

y1 = (-4-10)/2 = -7 < 0 - не интересно

y2 = (-4+10)/2 = 3 > 0

x1,2 = ±$\sqrt{3}$