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All Russian MO 2015 11 th grade, ineq.

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May 23, 2015
inequalities

Problem Statement

Let a,b,c,d be real numbers satisfying ∣a∣,∣b∣,∣c∣,∣d∣>1|a|,|b|,|c|,|d|>1 and abc+abd+acd+bcd+a+b+c+d=0abc+abd+acd+bcd+a+b+c+d=0. Prove that 1a−1+1b−1+1c−1+1d−1>0\frac {1} {a-1}+\frac {1} {b-1}+ \frac {1} {c-1}+ \frac {1} {d-1} >0
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