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MATH / Let r₁, r₂, …, r₇ be the distinct complex roots of the polynomial P(x)=x⁷−7. Let K=∏_(1≤i<j≤7)(r_(i)+r_(j)).In other words, K is the product of all numbers of the of the form …

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problem

Let r1,r_1, r2,r_2, …,\dots, r7r_7 be the distinct complex roots of the polynomial P(x)=x7−7.P(x) = x^7 - 7. Let K=∏1≤i<j≤7(ri+rj).K = \prod_{1 \le i < j \le 7} (r_i + r_j).In other words, KK is the product of all numbers of the of the form ri+rj,r_i + r_j, where ii and jj are integers for which 1≤i<j≤7.1 \le i < j \le 7. Determine K2.K^2.
Plain-text mathematical notation (without MathML)
Let r₁, r₂, …, r₇ be the distinct complex roots of the polynomial P(x)=x⁷−7.  Let
K=∏_(1≤i<j≤7)(r_(i)+r_(j)).In other words, K is the product of all numbers of the of the form r_(i)+r_(j), where i and j are integers for which 1≤i<j≤7.  Determine K².
Original LaTeX notation
Let $r_1,$ $r_2,$ $\dots,$ $r_7$ be the distinct complex roots of the polynomial $P(x) = x^7 - 7.$  Let
\[K = \prod_{1 \le i < j \le 7} (r_i + r_j).\]In other words, $K$ is the product of all numbers of the of the form $r_i + r_j,$ where $i$ and $j$ are integers for which $1 \le i < j \le 7.$  Determine $K^2.$

level

Level 5

type

Intermediate Algebra

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task_id
9690f309-00fc-52ab-bb76-337c71d63fc5
task_key
intermediate~5falgebra--test--9690f309-00fc-52ab-bb76-337c71d63fc5
task_revision_id
1
config / split
intermediate_algebra / test

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