If {x+(1/x)} = 2, then [(x^2)+[1/(x^2)]] = -2 is equal to ?
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If {x+(1/x)} = 2, then [(x^2)+[1/(x^2)]] = -2 is equal to ?
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Answer:
Given: (x + \frac{1}{x} = 2)
Step 1: Solve for (x): Multiply both sides of the equation by (x) to eliminate the fraction: (x^2 + 1 = 2x)
Rearrange the equation to form a quadratic equation: (x^2 - 2x + 1 = 0)
Factorize the quadratic equation: ((x - 1)^2 = 0)
Taking the square root of both sides: (x - 1 = 0)
Solve for (x): (x = 1)
Step 2: Substitute the value of (x) into (\left(x^2 + \frac{1}{x^2}\right)): (\left(1^2 + \frac{1}{1^2}\right) = \left(1 + 1\right) = 2)
Therefore, (\left(x^2 + \frac{1}{x^2}\right) = -2) is not equal to 2.
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