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Example Questions
Example Question #2 :How To Find A Solution Set
Give all real solutions of the following equation:
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 productand 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 #11 :How To Find A Solution Set
Give all real solutions of the following equation:
The equation has no real solutions.
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.
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