6t²-t-3=0 a=6 , b=-1,c=-3
по теореме Виета
t₁+t₂=-b/a
t₁*t₂=c/a
1) 1/t₁ + 1/t₂= (t₂+t₁)/t₁*t₂= (-b/a) / (c/a)
(-(-1)/6) / (-3)/6 = 1/6 *(-6/3)= -1/3
2) t₁²+t₂²=(t₁+t₂)²-2t₁t₂ =(-b/a)² -2*c/a
(-(-1)/6)² -2* (-3)/6= 1/36 +1 = 37/36
3) (t₁/t₂ + t₂/t₁) =(t₁²+t₂²)/t₁t₂= ((t₁+t₂)²-2t₁t₂) /t₁t₂= ((-b/a)² -2*c/a) /(c/a)
((-(-1)/6)² -2* (-3)/6) / -3/6 = 37/36 * -6/3 =-37/18
4) t₁³+t₂³=(t₁+t₂)(t₁²-t₁t₂+t₂²) =(t₁+t₂)((t₁+t₂)²-2t₁t₂-t₁t₂ )=(-b/a)*(-b/a)² -3*c/a)
(-(-1)/6)* ((-(-1)/6)² -3* (-3)/6) = 1/6 *( 1/36 + 9/6) =1/6 * 55/36 =55/ 216