If {x+(1/x)} = 2, then [(x^2)+{1/(x^2)}] = ?
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Answer:
To find the value of [(x^2) + (1/(x^2))], we can square the equation {x + (1/x)} = 2.
(x + (1/x))^2 = 2^2 (x + (1/x))^2 = 4
Expanding the left-hand side of the equation:
(x^2) + 2(x)(1/x) + (1/x)^2 = 4 (x^2) + 2 + (1/x^2) = 4
Now, subtract 2 from both sides:
(x^2) + (1/x^2) = 4 - 2 (x^2) + (1/x^2) = 2
Therefore, the value of [(x^2) + (1/(x^2))] is 2.
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