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--- pow:problem6f24 [2024/11/19 04:04] – created mazur
+++ pow:problem6f24 [2024/11/21 09:18] (current) – mazur
@@ Line 1: / Line 1: @@
+<box 85% round orange|Problem 6 (due on Monday, November 18). >
+For real numbers $a,b,c$ consider the system of equations
+\[x^2+2yz=a,\ \ y^2+2xz=b,\ \ z^2+2xy=c.\]
+Prove that this system has at most one solution in real numbers $x,y,z$ such that $x\geq y\geq z$ and
+$x+y+z\geq 0$. Prove that such a solution exists if and only if $a+b+c\geq 0$ and $b=\min(a,b,c)$.
+Here $\min(a,b,c)$ denotes the smallest number among $a,b,c$.
+</box>
+No solution were submitted. For a detailed solution see the following link {{:pow:2024fproblem6.pdf|Solution}}.