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Example Questions
Example Question #1 : Solving Equations And Inequallities
Give all real solutions of the following equation:
Possible Answers:
Correct answer:
Explanation:
By substituting
- and, subsequently, this can be rewritten as a quadratic equation, and solved as such:
We are looking to factor the quadratic expression as
, replacing the two question marks with integers with product and sum 5; these integers are .
Substitute back:
The first factor cannot be factored further. The second factor, however, can itself be factored as the difference of squares:
Set each factor to zero and solve:
Since no real number squared is equal to a negative number, no real solution presents itself here.
The solution set is
.Example Question #2 : Solving Equations And Inequallities
Give all real solutions of the following equation:
Possible Answers:
The equation has no real solutions.
Correct answer:
Explanation:
By substituting
- and, subsequently, this can be rewritten as a quadratic equation, and solved as such:
We are looking to factor the quadratic expression as
, replacing the two question marks with integers with product 36 and sum ; these integers are .
Substitute back:
These factors can themselves be factored as the difference of squares:
Set each factor to zero and solve:
The solution set is
.
David
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