Given real numbers $a,\,b,\,c$ such that
$a^2+ab+b^2=2$, $b^2+bc+c^2=3$, $c^2+ca+a^2=5$
Evaluate $ab+bc+ca$.
I hope you would try this problem out and attempt it in every way you could. Break this problem down into smaller cases and solve each piece, experience the process and conquer it!
I will post the suggested solution soon. See you!
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