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Re: Maths Olympiad Previous year Questions
Here I am providing the list of few questions of Regional Mathematical Olympiad exam question paper which you are looking for . 1. Let AC be a line segment in the plane and B a point between A and C. Construct isosceles triangles PAB and QBC on one side of the segment AC such that \APB = \BQC = 120◦ and an isosceles triangle RAC on the otherside of AC such that \ARC = 120◦. Show that PQR is an equilateral triangle. 2. Solve the equation y3 = x3 + 8x2 − 6x + 8, for positive integers x and y. 4.All the 7-digit numbers containing each of the digits 1, 2, 3, 4, 5, 6, 7 exactly once, and not divisible by 5, are arranged in the increasing order. Find the 2000-th number in this list. For more questions , here is the attachment Regional Mathematical Olympiad exam question paper
__________________ Answered By StudyChaCha Member Last edited by Aakashd; August 2nd, 2018 at 12:03 PM. |
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Re: Maths Olympiad Previous year Questions
Well, as you want to get the Regional Mathematical Olympiad Exam Question Paper so here I am sharing this with you 1. Three positive real numbers a, b, c are such that a 2 + 5b 2 + 4c 2 − 4ab − 4bc = 0. Can a, b, c be the lengths of the sides of a triangle? Justify your answer. Solution No. Note that a 2 + 5b 2 + 4c 2 − 4ab − 4bc = (a − 2b) 2 + (b − 2c) 2 = 0 ⇒ a : b : c = 4 : 2 : 1 ⇒ b + c : a = 3 : 4. The triangle inequality is violated. 2. The roots of the equation x 3 − 3ax2 + bx + 18c = 0 form a non-constant arithmetic progression and the roots of the equation x 3 + bx2 + x − c 3 = 0 form a non-constant geometric progression. Given that a, b, c are real numbers, find all positive integral values of a and b. Regional Mathematical Olympiad Exam Question Paper
__________________ Answered By StudyChaCha Member Last edited by Aakashd; August 2nd, 2018 at 12:03 PM. |