Lesson Entertainment problems on quadratic equations

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Entertainment problems on quadratic equations

Problem 1

The correct addition 13 + 24 + 43 + 44 = 102 looks strange because it is in another base.
What is the base?

Solution

    +--------------------------------------------------------+
    |     Looking at the last digits of these numbers,       |
    |  you notice that neither 2, nor 3 nor 4 is the base.   |
    +--------------------------------------------------------+


Let the base be "b".  Then we can write this equation

    (b+3) + (2b+4) + (4b+3) + (4b+4) = .


Simplify and write in standard form of quadratic equation

    11b + 14 =  + 2

     - 11b - 12 = 0


Solve by factoring

    (b-12)*(b+1) = 0


The appropriate solution/answer is  b= 12.

Solved.

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It is nice entertainment problem with non-standard setup.

And making right setup is the most engaging part of its solution.

My other lessons on quadratic equations in this website are
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    - HOW TO solve quadratic equation by completing the square - Learning by examples
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    - OVERVIEW of lessons on solving quadratic equations

Use this file/link ALGEBRA-I - YOUR ONLINE TEXTBOOK to navigate over all topics and lessons of the online textbook ALGEBRA-I.

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