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Proofs of example 8:
Suppose that a, b, c, , and are real numbers, with the following conditions: , , k is any integer.
Prove that .
From (6), we have:
Squaring (9) and adding it to (10), we have:
From equations (5) and (6), we have:
where satisfies , or (if a = 0).
(3) - (4)
Since , . Hence (6) holds. From equations (5) and (6) we have:
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