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Question: a² + 1/a² = 23
Find the value of a + 1/a ?
Solution:
As we know, (a + b)² = a² + b² + 2ab
So, a² + b² = (a + b)² - 2ab
Now, Suppose b = 1/a, then the formula changes to:
a² + 1/a² = (a + 1/a)² - 2a(1/a)
23 = (a + 1/a)² - 2a/a
23 = (a + 1/a)² - 2
(a + 1/a)² = 23 + 2 = 25
Thus, (a + 1/a) = ±5
Hence, (a + 1/a) = (+5), and (-5)
So we got 2 answers of (a + 1/a)
(if you still have any doubt, feel free to comment.)
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thanks for free points
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