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MATH / Let a₁, a₂, …, a₁₂ be real numbers such that a₁+a₂+…+a₁₂=1. Find the minimum value of a₁²+a₂²+…+a₁₂².

Problem

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problem

Let a1,a_1, a2,a_2, …,\dots, a12a_{12} be real numbers such that a1+a2+…+a12=1.a_1 + a_2 + \dots + a_{12} = 1. Find the minimum value of a12+a22+…+a122.a_1^2 + a_2^2 + \dots + a_{12}^2.
Plain-text mathematical notation (without MathML)
Let a₁, a₂, …, a₁₂ be real numbers such that a₁+a₂+…+a₁₂=1.  Find the minimum value of
a₁²+a₂²+…+a₁₂².
Original LaTeX notation
Let $a_1,$ $a_2,$ $\dots,$ $a_{12}$ be real numbers such that $a_1 + a_2 + \dots + a_{12} = 1.$  Find the minimum value of
\[a_1^2 + a_2^2 + \dots + a_{12}^2.\]

level

Level 3

type

Intermediate Algebra

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Source and history

task_id
8348e2f2-92d8-5d3f-a306-c142af32cd68
task_key
intermediate~5falgebra--test--8348e2f2-92d8-5d3f-a306-c142af32cd68
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import