MathDB

12

Part of 2002 National Olympiad First Round

Problems(1)

P12 [Algebra] - Turkish NMO 1st Round - 2002

Source:

8/8/2014
What is the least possible value of ab+bc+acab + bc + ac such that a2+b2+c2=1a^2 + b^2 + c^2 = 1 where a,b,ca,b,c are real numbers?
<spanclass=′latex−bold′>a)</span> −1<spanclass=′latex−bold′>b)</span> −12<spanclass=′latex−bold′>c)</span> −13<spanclass=′latex−bold′>d)</span> −122<spanclass=′latex−bold′>e)</span> 0 <span class='latex-bold'>a)</span>\ -1 \qquad<span class='latex-bold'>b)</span>\ -\dfrac 12 \qquad<span class='latex-bold'>c)</span>\ -\dfrac 13 \qquad<span class='latex-bold'>d)</span>\ -\dfrac{1}{2\sqrt 2} \qquad<span class='latex-bold'>e)</span>\ 0