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Omni-MATH / Let n be a given positive integer. Solve the system

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Let nn be a given positive integer. Solve the system x1+x22+x33+⋯+xnn=n,x_1 + x_2^2 + x_3^3 + \cdots + x_n^n = n, x1+2x2+3x3+⋯+nxn=n(n+1)2x_1 + 2x_2 + 3x_3 + \cdots + nx_n = \frac{n(n+1)}{2} in the set of nonnegative real numbers.
Plain-text mathematical notation (without MathML)
Let n be a given positive integer. Solve the system 
x₁+x₂²+x₃³+⋯+x_(n)^(n)=n,
x₁+2x₂+3x₃+⋯+nx_(n)=(n(n+1))/(2)
in the set of nonnegative real numbers.
Original LaTeX notation
Let $n$ be a given positive integer. Solve the system 
\[x_1 + x_2^2 + x_3^3 + \cdots + x_n^n = n,\]
\[x_1 + 2x_2 + 3x_3 + \cdots + nx_n = \frac{n(n+1)}{2}\]
in the set of nonnegative real numbers.

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Source and history

task_id
bec5c780-12fd-57d0-aa68-4541222ef373
task_key
test--bec5c780-12fd-57d0-aa68-4541222ef373
task_revision_id
1
config / split
/ test

Official source

initial import