Maths Olympiad Daily Problems

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

Hey members 👋🏻 This problem is open till two weeks and once the correct solution is recieved the submission will be closed and the first correct solver will be regarded as co author of this problem Solution to to shared on my dm or Gmail: theimomedalist@gmail.com