1)x^4-(a^2+9)x^2+9a^2=0
y=x²
y²-(a²+9)y+9a²=0
D=(a²+9)²-4*9a²=a⁴+18a²+91-36a²=a⁴-18a²+91=(a²-9)²
y₁=(a²+9-(a²-9))/2=18/2=9 x₁=3 x₂=-3
y₂=(a²+9+(a²-9))/2=2a²/2=a² x₃=a x₄=-a
2)x^4-(9a^2+4)x^2+36a^2=0
y=x²
y²-(9a²+4)y+36a²=0
D=(9a²+4)²-4*36a²=81a⁴+72a²+16-144a²=81a⁴-72a²+16=(9a²-4)²
y₁=(9a²+4-(9a²-4))/2=8/2=4 x₁=2 x₂=-2
y₂=(9a²+4+9a²-4)/2=9a² x₃=-3a x₄=3a
3)(x-1)^4-x^2+2x-73=0
(x-1)⁴-(x²-2x+1)-72=0
(X-1)⁴-(x-1)²-72=0
y=(x-1)²
y²-y-72=0
D=1-4*72=289=17²
y₁=(1-17)/2=-8
y₂=(1+17)/2=9
(x-1)²=-8 нет решений
(x-1)²=9
x-1=3 x-1=-3
x₁=4 x₂=-2
4)(x+2)^4+2x^2+8x-16=0
(x+2)⁴+2(x²+4x+4)-8-16=0
(x+2)⁴+2(x+2)²-24=0
(x+2)²=y
y²+2y-24=0
D=2²+4*24=100
y₁=(-2+10)/2=4
y₂=(-2-10)/2=-6
(x+2)²=-6 нет решений
(x+2)²=4
x+2=2
x₁=0
x+2=-2
x₂=-4