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Simultaneous equations in n variables

Source: Czech-Polish-Slovak 2005 Q1

April 27, 2013
algebrapolynomialcalculusderivativefunctionanalytic geometrygraphing lines

Problem Statement

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.
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