MathAdvanced Math
Practice
Nonlinear Equations Practice
Original questions solving quadratics and checking nonlinear solutions.
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Question 1 of 2
Question 1
Medium
Correct answer\(x=3\text{ and }x=4\)
Explanation
Factor: \(x^2-7x+12=(x-3)(x-4)\). The zero-product property gives \(x=3\) or \(x=4\).
Question 2 of 2
Question 2
Hard
Correct answer\(3\)
Explanation
Squaring gives \(x+1=(x-1)^2\), so \(x(x-3)=0\). Checking the candidates in the original equation eliminates \(0\) and confirms \(3\).
- Generate candidates
\(x+1=x^2-2x+1\Rightarrow x(x-3)=0\)
- Check
\(\sqrt{3+1}=3-1=2\)
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Questions to review
No mistakes this time. Excellent work.
- Question 1Solve a quadratic by factoringMedium
- Question 2Solve a radical equationHard