APPROXIMATE FORMULAS FOR THE ROOTS OF CUB IC EQUATIONS IRREDUCIBLE CASE

For equation z(3)-az+b=0 with real a>0, b in irreducible case (b(2)/a( 3) less than or equal to 4/27=c(0)(2)) approximate algebraic expressio ns for all three,roots as functions oi a, b are obtained. They are muc h more simple than trigonometric exact solution. By b>0, z(1)=-1,0039 root a- -0,4019b/a(delta<3,7 . 10(-3)), z(2)=root a+0,11b/a-0,465 xi(d elta<8,7.10(-4)), z(3)=0,3734b/a- -0,2117b(2)/root a(5)+0,465 xi(delta <3,7.10(-3)) where xi=root a-root a-b/c(0) root a, delta is the maxima l relative error of solution. Also other expressions for the roots are obtained. For b<0 the roots are received from relation z(-b)=-z(b).