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for question related to conjectures.

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A seemingly simple inequality

Let $a_i,b_i\in\mathbb{R}$ and $n>1$, does the inequality $$ \left(\sum_{i=1}^n a_i^2\right)\left(\sum_{i=1}^n b_i^2\right)+\left(\sum_{i=1}^na_i b_i\right)^2\ge \sqrt{\left(\sum_{i=1}^n a_i^4\right) …
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