1) (x^2+4) ^2 + (x^2+4) - 30=0

2) (x^2-8) ^2+3,5 (x^2-8) - 2=0

3) (1-x^2) ^2+3,7 (1-x^2) + 2,1=0

4) (1+x^2) ^2+0,5 (1+x^2) - 5=0

1) (x^2+4) = a

a^2+a-30=0

a1+a2=-p=-1

a1*a2=q=-30

a1=5

a2=-6

x^2+4=5

x^2=5-4=1

x1=1

x2=-1

x^2+4=-6

x^2=-6-4=-10-посторонний корень.

2) (x^2-8) = a

a^2+3,5a-2=0

D=3,5^2-4*1 * (-2) = 12,25+8=20,25=4,5^2

a1 = (-3,5+4,5) / 2*1=1/2

a2 = (-3,5-4,5) / 2 = (-8)

x^2-8=a1=1/2

x^2=1/2+8=0,5+8=8,5

x1=√8,5

x2=-√8,5

x^2-8=a2=-8

x^2=-8+8=0

x=0

3) (1-x^2) = a

a^2-3,7a+2,1=0

D = (-3,7) ^2-4*1*2,1=13,69-8,4=5,69=2,3^2

a1 = (- (-3,7) + 2,3) / 2*1 = (3,7+2,3) / 2=6/2

a1=3

a2 = (- (-3,7) - 2,3) / 2 = (3,7-2,3) / 2=1,4/2

a2=0,7

1-x^2=a1=3

-x^2=3-1=2

x^2=-2-нет корней

1-x^2=a2=0,7

-x^2=0,7-1=-0,3

x^2=0,3

x1=√0,3

x2=-√0,3

4) (1+x^2) = a

a^2+0,5a-5=0

D=0,5^2-4*1 * (-5) = 0,25+20=20,25=4,5^2

a1 = (-0,5+4,5) / 2*1=4/2

a1=2

a2 = (-0,5-4,5) / 2 = (-5) / 2

a2=-2,5

1+x^2=a1=2

x^2=2-1=1

x1=1

x2=-1

1+x^2=a2=-2,5

x^2=-2,5-1=-3,5

x^2=-3,5-посторонний корень