DA PHUC HIGH SCHOOL MATHS TEST GRADE: 10 School year: 2012-2013 Time allowance: 90 minutes - SOLUTION Notice that: then That is Let we get which is equivalent to Since , we have: Thus -3 -1 -2 then 3 is a perfect square -1 -3 -2 From , we implies So Hence The equation is equivalent to Let then Hence, we get Solving that equation, we have With then With Solving for then // that is Solving for The equation has solutions {1; Draw or } By Thales theorem, we have That is that is A We also have B K E D C From , interchanging with gives So we have the system of equations: Solving the system, we get Therefore, We have = = So we get the desired result We have x A D E B C Chose a point D on AE such that AD = AB = 3cm The isosceles triangle has so it is an equilateral triangle That is BD = AB = 3cm and We get BD//AC ( Therefore AE =12cm .By Thales theorem, we have We have (by the Cauchy inequality) Similarly, we also have The inequality is proved Equality occurs when 10 .(*) If then If then , implies From (*), we get So