414 Dr. button on Cubic 'Equations' 
- SJI - I v/ -7, j = + c = + 4 v/-7 - 
- | + -7, and y / - \/ b — c - v^f -» f\/ -7 = 
- f — 7 . Hence r =■ r + d — 3 the middle root 
and - 
J -f* <l/ 
V- 
~ 2 
2 
is /- 7 .V - 3 =fcSlH 
the greateft and leaft roots. 
63. Ex. 8. Again, from the equation x % - 1 2X- 
- Sv 7 2, we have a = - 4, and b - - 4-^2 ; hence r = 
+ a 1 — ^32 - 64 =■ >/ —32 = 4%/ -2, s —■‘Vb + c - 
— 2 + 4 V 7 - 2 = \/ 2 + 2, and d — s/i^sZ—i.. 
So that r — s + d — 1/2 the middle root; and 
— Li-?' t — ? \/ — 3 = — s/ 2 =s v^— a . \/— 3 = 
2 2 J J 
— \/ 2 ± %/ 6 = - 2 . 1 =f \/ 3 the greateft and leaft roots. 
64. Ex. 9. But the equation x 3 - 15^= 22 gives 
= - 5, and b — 1 1 ; and therefore c — \/ b z + a 1 
= v / 121 - 125 = \/ -4, r = + t = v / ii + -s/ —4 = 
-t - \/-4,. and d — - 1 + ^-4. Confequently 
r = r + ^= -2 the leaft root; and - — — ± — 3 
’ 2 2 a 
= 1 ±\Z-4.i/-3 = 1 ± v 7 i 2 the two greater roots. 
65. Ex. 10. Laftly, in the equation x 3 - 152; = 20, 
we have a - - 5, and b — 10; confequently c - + a 3 
= ^ 100 - 125 = v 7 - 25 = 5 %/ t, j = + c = 
v' to + 5\/-i , and ^ = ^10- 5\/-i. Therefore 
r 
y>* 
