MathDB

13

Part of 2023-24 IOQM India

Problems(1)

IOQM 2023-24 P-13

Source:

9/3/2023
The ex-radii of a triangle are 1012,1210\frac{1}{2}, 12 and 1414. If the sides of the triangle are the roots of the cubic x3−px2+qx−r=0x^3-px^2+qx-r=0, where p,q,rp, q,r are integers , find the nearest integer to p+q+r.\sqrt{p+q+r}.