MathDB
VMO-D2-P5

Source: VMO-2020 D2-P5

December 28, 2019
system of equationsalgebra

Problem Statement

Let a system of equations: {x−ay=yzy−az=zxz−ax=xy\left\{\begin{matrix}x-ay=yz\\y-az=zx\\z-ax=xy\end{matrix}\right. a)Find (x,y,z) if a=0 b)Prove that: the system have 5 distinct roots ∀\foralla>1,a∈R.\in\mathbb{R}.
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