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Leni [432]
3 years ago
13

What is the maximum number of possible solutions for the system shown below?

Mathematics
1 answer:
julsineya [31]3 years ago
7 0

\bf \begin{cases} 3x^2+y^2=4\\[-0.5em] \hrulefill\\ x^2+y=5\implies \boxed{y}=5-x^2 \end{cases} \\\\\\ \stackrel{\textit{substituting \boxed{y} in the 1st equation}}{3x^2+\left( \boxed{5-x^2} \right)^2=4}\implies 3x^2+25-10x^2+x^4=4 \\\\\\ x^4-8x^2+21=0\impliedby \begin{array}{llll} \textit{the degree of this polynomial}\\ \textit{is 4, and by the fundamental}\\ \textit{theorem of algebra, it can}\\ \textit{have \boxed{4} solutions at most} \end{array}

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