Lesson Entertainment problems on quadratic equations
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<H2>Entertainment problems on quadratic equations</H2> <H3>Problem 1</H3>The correct addition 13 + 24 + 43 + 44 = 102 looks strange because it is in another base. What is the base? <B>Solution</B> <pre> +--------------------------------------------------------+ | 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) = {{{b^2 +2}}}. Simplify and write in standard form of quadratic equation 11b + 14 = {{{b^2}}} + 2 {{{b^2}}} - 11b - 12 = 0 Solve by factoring (b-12)*(b+1) = 0 The appropriate solution/answer is b= 12. </pre> Solved. ------------------ It is nice entertainment problem with non-standard setup. And making right setup is the most engaging part of its solution. 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