Round 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 is true, the formula for half-companion Pell numbers includes a plus or minus one in the (-5[1])numerator. This fact can be shown by stating that [read slowly] a squared is equal to two b squared and then finding a (*) contradiction because (10[1])a and b (10[1])must be coprime. (10[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. Angry Pythagoreans legendarily murdered Hippasus for proving, for 10 points, what fact (10[1])that says a number beginning with (10[1])1.414 is not a ratio of integers? ■END■

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