Question
If $$x + \frac{1}{x} = 1,$$ then the value of $$\frac{2}{{{x^2} - x + 2}} = \,?$$
Answer: Option B
$$\eqalign{
& {\text{Given, }}x + \frac{1}{x} = 1 \cr
& {\text{Find }}\frac{2}{{{x^2} - x + 2}} = ? \cr
& x + \frac{1}{x} = 1 \cr
& {x^2} + 1 = x \cr
& \left( {{x^2} - x} \right) = - 1 \cr
& {\text{Putting value in,}} \cr
& = \frac{2}{{{x^2} - x + 2}} \cr
& = \frac{2}{{ - 1 + 2}} \cr
& = 2 \cr} $$
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$$\eqalign{
& {\text{Given, }}x + \frac{1}{x} = 1 \cr
& {\text{Find }}\frac{2}{{{x^2} - x + 2}} = ? \cr
& x + \frac{1}{x} = 1 \cr
& {x^2} + 1 = x \cr
& \left( {{x^2} - x} \right) = - 1 \cr
& {\text{Putting value in,}} \cr
& = \frac{2}{{{x^2} - x + 2}} \cr
& = \frac{2}{{ - 1 + 2}} \cr
& = 2 \cr} $$
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