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August 26th, 2016, 06:53 AM   #1
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Arithmetic Progression

Hey , guys ! Can you help me solve this problem ?
Find x∈R , if x²-5x+6 ; -x²-3x+3 ; 2x²-4x+9 and x²+8x-5 are in an arithmetic progression . Thank you very much .
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August 26th, 2016, 01:48 PM   #2
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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 term-first term=third term-second term=fourth term-third 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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