\(2x + \frac{2}{x} = 3\) হলে, \({x^2} + \frac{1}{{{x^2}}}\) এর মান কত ?
Solution
Correct Answer: Option B
Solution:
\(2x + \frac{2}{x} = 3\) => \(2(x + \frac{1}{x}) = 3\) => \({(x + \frac{1}{x})^{2\;}} = {(\frac{3}{2})^{2\;}}\)
=> \({x^{2\;}} + \frac{1}{{{x^{2\;}}}} + 2 \times x \times \frac{1}{x} = \frac{9}{4}\) => \({x^{2\;}} + \frac{1}{{{x^{2\;}}}} = \frac{9}{4} - 2\)
=> \({x^{2\;}} + \frac{1}{{{x^{2\;}}}} = \frac{{9 - 8}}{4} = \frac{1}{4}\) \({x^{2\;}} + \frac{1}{{{x^{2\;}}}} = \frac{1}{4}\)
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