One author (Bunt) says, “the Pythagoreans were familiar with the formula:

(m2+12)2=(m212)2+m2\displaystyle {\left(\frac{{{m}^{{2}}+{1}}}{{2}}\right)}^{{2}}={\left(\frac{{{m}^{{2}}-{1}}}{{2}}\right)}^{{2}}+{m}^{{2}}

where m\displaystyle {m} is an odd natural number.” This formula is related to Pythagorean triples.

A) Show that this formula works for m=11\displaystyle {m}={11}. Show all work on your hand-in sheet.

B) Bunt also says "the equality may be checked readily." In part (A) you checked it for a specific value of m\displaystyle {m}. Show that it’s true for any and ALL values of m\displaystyle {m}. Show all steps and work. Hint: To prove this, do NOT replace m\displaystyle {m} with any specific numbers. Instead, start with the general equation and use algebra to simplify both sides of the equation until you can show that both side are equivalent/equal to each other. (Be careful when multiplying these expressions out. A common error is to say that (m2+1)2=m4+1\displaystyle {\left({m}^{{2}}+{1}\right)}^{{2}}={m}^{{4}}+{1}, which is false!)

You need to SHOW your work for this problem carefully. Try to show all parts on one side of one sheet. You should start your work at the top of a clean sheet of lined paper...write your name and the problem number at the top of the page. Your work should be neat and organized so that I can understand your steps and your logic. Label all parts clearly. When you are done, take a picture of your work with a camera or scan your work into picture form. Then upload the file using the "Choose File" button to find your file on your computer. This problem will not be fully graded until after the assignment due date...your score may go up or down based on your hand work.

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