Packet 6: Tossup 18

Description Required. Stanley Tennenbaum proved this fact using a diagram where 2 squares overlap to create the [read slowly] quantity two b minus a squared. (-5[1])Because this fact (-5[1])is true, the formula for half-companion Pell numbers includes a plus or minus one in the (-5[1])numerator. (15[1])This fact can be shown by stating that [read slowly] a squared is equal to two b (15[1])squared (15[1])and then (-5[1])finding a (15[1])(*) contradiction (10[3])because (10[1])a and b (10[4])must (10[2])be (10[3])coprime. (10[5]-5[2])Applying the rational root test (10[1])to the equation x squared (10[1])minus two equals zero can be used to prove this fact. (10[1])Angry Pythagoreans (10[1])legendarily (10[1])murdered (10[1])Hippasus (10[1]-5[2])for proving, (10[2]-5[2])for 10 points, what fact (10[1]-5[1])that says a number (10[1])beginning with (10[1])1.414 is not a ratio of integers? ■END■ (10[6]0[4])

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