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TOT 1998 Spring OS4 x^2 + y^2 +z^2= X and $|x| + |y| +|z| = D

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May 11, 2020
algebrasystem of equations

Problem Statement

For some positive numbers A,B,CA, B, C and DD, the system of equations {x2+y2=A∣x∣+∣y∣=B\begin{cases} x^2 + y^2 = A \\ |x| + |y| = B \end{cases} has mm solutions, while the system of equations {x2+y2+z2=X∣x∣+∣y∣+∣z∣=D\begin{cases} x^2 + y^2 +z^2= X\\ |x| + |y| +|z| = D \end{cases} has nn solutions. If m>n>1m > n > 1, find mm and nn.
( G Galperin)
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