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Omni-MATH / Let a_(i),b_(i),i=1,⋯,n are nonnegitive numbers,and n≥4,such that a₁+a₂+⋯+a_(n)=b₁+b₂+⋯+b_(n)>0. Find the maximum of (∑_(i=1)^(n)a_(i)(a_(i)+b_(i)))/(∑_(i=1)^(n)b_(i)(a_(i)+b_(i)))

Problem

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problem

Let

a_i,b_i,i=1,\cdots,n

are nonnegitive numbers,and

n\ge 4

,such that

a_1+a_2+\cdots+a_n=b_1+b_2+\cdots+b_n>0

. Find the maximum of

\frac{\sum_{i=1}^n a_i(a_i+b_i)}{\sum_{i=1}^n b_i(a_i+b_i)}

Plain-text mathematical notation (without MathML)

Let a_(i),b_(i),i=1,⋯,n are nonnegitive numbers,and n≥4,such that a₁+a₂+⋯+a_(n)=b₁+b₂+⋯+b_(n)>0.

Find the maximum of (∑_(i=1)^(n)a_(i)(a_(i)+b_(i)))/(∑_(i=1)^(n)b_(i)(a_(i)+b_(i)))

Original LaTeX notation

Let $a_i,b_i,i=1,\cdots,n$ are nonnegitive numbers,and $n\ge 4$,such that $a_1+a_2+\cdots+a_n=b_1+b_2+\cdots+b_n>0$.

Find the maximum of $\frac{\sum_{i=1}^n a_i(a_i+b_i)}{\sum_{i=1}^n b_i(a_i+b_i)}$

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task_id: a9439e31-8c5a-524f-99e9-0f7d9badac56
task_key: test--a9439e31-8c5a-524f-99e9-0f7d9badac56
task_revision_id: 4
config / split: / test

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