б) 4(z + 1)^3 - 2z(2z
+ 1)^2 + 4z^2(z – 1) = 24;
4(z^3+3z^2+3z+1)-2z(4z^2+4z+1)+4z^2(z-1)
= 24
4z^3+12z^2+12z+4-8z^3-8z^2-2z+4z^3-4z^2
= 24
10z+4 = 24
10z = 20
z=2
а) (х + 2)^3 – (х – 3)^3 = 15х^2 – 85
(x+2-x+3)((х+2)^2+(х+2)(х-3)+(х-3)^2) = 5(3х^2-17)
5(x^2+4x+4+x^2-3x+2x-6+x^2-6x+9) = 5(3х^2-17)
3x^2-3x+7 = 3х^2-17
-3x+7=-17
3x=17+7
3x=24
x=8
г) 27 + 7а(9 + 7а)^2 = (7а + 6)^3.
27+7a(81+126a+49a^2)
= 343a^3+882a^2+756a+216
27+567a+882a^2+343a^3
= 343a^3+882a^2+756a+216
343a^3+882a^2+756a+216-27-567a-882a^2-343a^3
= 0
189a+189 =
0
189a=-189
a=-1
в) 8x^3 – 36х^2 + 54х – 27 = 0;
(8x^3-27)-18x(2x-3) = 0
(2x-3)(4x^2+6x+9)-18(2x-3) = 0
(2x-3)(4x^2+6x+9-18) = 0
2x-3=02x=3
x =
3/2
x1 =
1,5
4x^2+6x+9-18 = 0
4x^2+6x-9 = 0
4x^2+12x-6x+9-18 = 0
(2x+3)^2-3(2x+3) = 0
(2x+3)(2x+3-3) = 0
2x+3=0
x= -3/2
x2=-1,5
2x=0
x3=0