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Another interesting problem

Algebra Level 3

If \(a,b\) and \(c\) are real numbers satisfying \(a^2+b^2+ c^2=1\), which of the following inequalities is true?

\[- \frac{1}{2} \leq ab+ac+bc \leq 1\] \[b(a+c)\geq ac\] \[(ab+bc+ac)^2 \geq 2\] \[ab+ac+bc \geq 0\]

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Excel in math and science

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by Mr Yovan

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