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MATH / Let x₁, x₂, …, x₁₀₁ be positive real numbers such that x₁²+x₂²+…+x₁₀₁²=1. Find the maximum value of x₁x₂+x₁x₃+…+x₁x₁₀₁.

Problem

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problem

Let x1,x_1, x2,x_2, …,\dots, x101x_{101} be positive real numbers such that x12+x22+…+x1012=1.x_1^2 + x_2^2 + \dots + x_{101}^2 = 1. Find the maximum value of x1x2+x1x3+…+x1x101.x_1 x_2 + x_1 x_3 + \dots + x_1 x_{101}.
Plain-text mathematical notation (without MathML)
Let x₁, x₂, …, x₁₀₁ be positive real numbers such that x₁²+x₂²+…+x₁₀₁²=1.  Find the maximum value of
x₁x₂+x₁x₃+…+x₁x₁₀₁.
Original LaTeX notation
Let $x_1,$ $x_2,$ $\dots,$ $x_{101}$ be positive real numbers such that $x_1^2 + x_2^2 + \dots + x_{101}^2 = 1.$  Find the maximum value of
\[x_1 x_2 + x_1 x_3 + \dots + x_1 x_{101}.\]

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
bf58a051-8b91-5c70-8e39-afd75cd90f2e
task_key
intermediate~5falgebra--test--bf58a051-8b91-5c70-8e39-afd75cd90f2e
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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