Describe this pattern. Then see if you can think of another Pythagorean triple that doesn't follow the pattern you just described and that can't be generated using the identity (x2 − 1)2 + (2x)2 = (x2 + 1)2. Explain your findings. x-value Pythagorean Triple 7 (14,48,50) 8 (16,63,65) 9 (18,80,82) 10 (20,99,101)

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Step-by-step explanation:

A Pythagorean triple is a set of 3 positive integer numbers, a, b, and c which satisfies the Pythagorean theorem:

Given the identity:

We verify that the numbers given table are Pythagorean triples.

Next, we examine the pattern:

From the pattern, our first number is 2x, the second number is x² - 1, and the third number(hypotenuse) is x² + 1

Next, we show that  (x² - 1)² + (2x)² = (x² + 1)² is an identity

Since Left Hand Side=Right hand Side. For all x, the equation is always true.

Therefore, the pattern is true for any Pythagorean triple.

there are no short passages to look at

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step-by-step explanation: