Question

Помогите решить уравнения!!!
а) (х + 2)^3 – (х –
3)^3 = 15х^2 –
85;                      

б) 4(z + 1)^3                
                       – 2z(2z + 1)^2 + 4z^2(z – 1) = 24;

в) 8x^3 – 36х^2 + 54х – 27
= 0;                              г) 27 +
7а(9 + 7а)^2 = (7а + 6)^3.

 

Answer 1

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=0 2x=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