Mathematics, 04.07.2019 22:30 dogskid1937
What is the maximum number of possible solutions for the system shown below? 3x^2+ y^2= 4 x^2 + y= 5 a. 1 b. 2 c. 4 d. 3
Answers: 1
![\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}](/tpl/images/0051/8135/3cdb0.png)
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What is the maximum number of possible solutions for the system shown below? 3x^2+ y^2= 4 x^2 + y...
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