Multiple Choice Question (MCQ)
What is the solution set to the equation 4+x^2=2x^2-5 ?
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×
\{x:x=3\}
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×
\{x:x=-3\}
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✓
\{x:x=\pm3\}
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×
\{x:x=-1\}
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×
\{x:x=1\}
Answer
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A solution set is the set of variables that makes the equation true. For a quadratic equation, it has either 2 duplicate roots(1 solution) or distinct roots.
Solving the equation gives
4+x^2=2x^2-5
x^2=9
Taking the square roots
x=\pm3
It turns out the equation has two distinct solutions. So the solution set of the equation is \{x:x=\pm3\} .
C is the correct choice.