Problem 2. Prove that there are infinitely many positive integer triples (x, y, z) such that x² + 2y² = 3x². Hint. Find an appropriate rational point that will act as a "pivot", much like in the case of classifying Pythagorean triples that we saw in this lecture.

Q: 4. Solve. A) 3 ()² − 7 (¹) + 4 = 0

A: Since you have posted multiple questions i can do first question as per our company guidelines…

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Q: 5) If you know the roots for a polynomial are x = -3, 1, and 2   which of the following could be the…

A: Given: If you know the roots for a polynomial are x = -3, 1, and 2 which of the following could be…

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Q: 1. Solve the rational inequalities x+1 a) X-3 х-2 b) x² - 4x c) _> 2 X-1

A: If we have a rational expression equal to and we want to know when this expression will be positive…

Q: 3) (- .) How many ordered quadruplets (a1, a2, a3, a4) of non-negative integers, where at least one…

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Q: 3) Suppose that f mx² + ax + bdx = m, a, & b are constants and C is an arbitrary constant. For each…

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Q: 2. Factor. a) x² 18x + 81 b) x² - 2x - 15 c) x² + 2x - 24 d) x² + 6x-40 e) x²+x-30 f) x² + 3x-35 g)…

A: Please follow the next step.

Q: 1. State the zeros of each by first rewriting the equation in factored form: a) y= x² - 6x – 16 b) y…

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A: We can solve this by using given information

Q: Find all solutions to the equation 2sin²(x) + 3sin(x) - 1 = 0 for -π ≤ x ≤ TT.

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