Maths Olympiad Exam

Suppose P is an interior point of a triangle ABC such that the ratios
d(A,BC)
d(P,BC)
,
d(B,CA)
d(P,CA)
,
d(C,AB)
d(P,AB)

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Maths Olympiad Other Question

Find the number of ordered triples (x, y, z) of nonnegative integers satisfying the
conditions:
(i) x = y + z;
(ii) x + y + z = 100. Find all real numbers a for which the equation
x^2 + (a + 2)x + 1 = 3|x| has exactly three distinct real solutions in x.