2(6х+5)^2(3х+2)(х+1)=1
2*(36х²+60х+25)*(3х²+2х+3х+2)=1
(36х²+60х+25)*(6х²+10х+4)=1
(36х²+60х+24 +1)*(6х²+10х+4)=1
(6*(6х²+10х+4)+ 1 )*(6х²+10х+4)=1
(6*(6х²+10х+4)² + (6х²+10х+4)-1 =0 замена (6х²+10х+4)=а
6а²+а-1=0
D=1+24=25 √D=5
a₁=(-1+5)/12 =1/3
a₂=(-1-5)/12 =-1/2
(6х²+10х+4)= 1/3 |*3 (6х²+10х+4)= -1/2 | *2
18x²+30x+12=1 12х²+20х+8=-1
18x²+30x+11=0 12х²+20х+9=0
D=900-792=108 D=400-432=-32 <0 решений нет<br>√D=√108 =√(36*3)=6√3
x₁=(-30+6√3)/36= (-5+√3)/6
x₂=(-30-6√3)/36= - (5+√3)/6