SOLUTION: If x = 2 - √2, evaluate x2 + 1/x2

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Question 1161885: If x = 2 - √2, evaluate x2 + 1/x2
Answer by Alan3354(69443) About Me  (Show Source):
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If x = 2 - √2, evaluate x2 + 1/x2
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Use ^ (Shift 6) for exponents.
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If x = 2 - √2, evaluate x^2 + 1/x^2
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x^2 = 2^2 - 4sqrt(2) + 2 = 6 - sqrt(32)
---> (6 - sqrt(32)) + 1/(6 - sqrt(32))
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= (6 - sqrt(32)) + (6 + sqrt(32))/(36 - 32)
= (6 - sqrt(32)) + (6 - sqrt(32))/4
= 5(6 - sqrt(32))/4
= 5(3 - sqrt(8))
= 15 - sqrt(200)