Maths Olympiad Daily Problems

Try ! IQOM 2 marker level question!

If the expression is equal to ae + b/e + c where a,b,c belong to Z Find the value of a²-b+c

Problem from Veer Re-formatted Let a, b, c and d be the zeroes of P(x) = 5x⁴ + px³ + qx² + rx + s and Let a, c and d be the zeroes of Q(x) = x³ - 9x² + tx - 24 If a, c and d are in AP and a, b, c and d are in HP, Find the value of |(P(1)/Q(1))|

Let a,b,c,d be zeroes of p(x)=5x⁴+px³+qx²+rx+s and a,c,d be the zeroes of q(x)=x³-9x²+tx-24 If a,c,d are in AP and a,b,c,d are in HP Find the value of | (p(1)/q(1)) |

A straight line through the vertex P of a triangle PQR intersects the side QR at the point S and circumcircle of triangle PQR at the point T. If S is not the centre of the circumcircle,then A) 1/PS + 1/ST < 2/√(QS×SR) B) 1/PS + 1/ST > 2/√(QS×SR) C) 1/PS + 1/ST <4/QR D) 1/PS + 1/ST >4/QR

Problem from Veer Jain *Edited due to typo errors* If a, b and c are the positive roots of the eqn x³ - 6x² + 3px - 2p = 0 , then find the value of a/b + b/c + c/a + abc

If a,b,c are the positive roots of the eqn x³-6x²+3px-2p then find the value of a/b + b/c + c/a + abc

a³/4b + b/8c² + (1+c)/2a ≥ x a,b,c are positive and x is the minimum value of the expression Find the value of 16x²

Question:-n^3pq - n is divisible by 3pq for which p and q are distinct primes, find smallest p+q