
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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August 26th, 2016, 06:53 AM  #1 
Newbie Joined: Aug 2016 From: Bucharest Posts: 14 Thanks: 0  Arithmetic Progression
Hey , guys ! Can you help me solve this problem ? Find x∈R , if x²5x+6 ; x²3x+3 ; 2x²4x+9 and x²+8x5 are in an arithmetic progression . Thank you very much . 
August 26th, 2016, 01:48 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,806 Thanks: 716 
For an arithmetic progression, the differences between successive terms is constant. You can then write two equations for x by taking pairs of differences to be equal, e.g. second termfirst term=third termsecond term=fourth termthird term. Each equation is a quadratic in x, so solve both (getting 2 roots in each case) and keep the root which is the same in both.


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