Difference between revisions of "2023 IOQM/Problem 13"
Combi-hater (talk | contribs) (Created page with "The ex-radii of a triangle are 10 1 2 , 12 and 14. If the sides of the triangle are the roots of the cubic x 3 − px2 + qx − r = 0 , where p, q, r are integers, find the in...") |
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| − | The ex-radii of a triangle are 10 1 | + | The ex-radii of a triangle are <math>10\frac{1}{2}</math>,<math>12</math> and <math>14</math>. |
| − | 2 | + | If the sides of the triangle are the roots of the cubic <math>x^3 - px^2 + qx - r</math> , where <math>p</math>, <math>q</math>, <math>r</math> are integers, find the integer |
| − | , 12 and 14. If the sides of the triangle are the | + | nearest to <math>\sqrt{p+q+r}</math> |
| − | roots of the cubic x | ||
| − | 3 | ||
| − | nearest to | ||
| − | p + q + r | ||
Latest revision as of 03:03, 16 December 2024
The ex-radii of a triangle are 
,
and 
.
If the sides of the triangle are the roots of the cubic 
, where 
, 
, 
are integers, find the integer
nearest to 
