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If x = 3 + 2√2, the value of \({x^2} + \frac{1}{{{x^2}}}\) is1). 362). 303). 324). 34 |
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Answer» Formula: (a – b)(a + b) = a2 – b2 Given, x = 3 + 2√2 $(\RIGHTARROW \frac{1}{x} = \frac{1}{{3 + 2\sqrt 2 }})$ Multiplying and dividing by 3 – 2√2 $(\Rightarrow \frac{1}{x} = \frac{{3 - 2\sqrt 2 }}{{\left( {3 + 2\sqrt 2 } \right)\left( {3 - 2\sqrt 2 } \right)}}\;)$ ⇒ 1/x = 3 – 2√2 $({\left( {x + \frac{1}{x}} \right)^2} = {x^2} + \frac{1}{{{x^2}}} + 2)$ $(\Rightarrow {\left( {3 + 2\sqrt 2+ 3 - \;2\sqrt 2 } \right)^2} - 2 = {x^2} + \frac{1}{{{x^2}}})$ $(\Rightarrow {x^2} + \frac{1}{{{x^2}}} = {6^2} - 2 = 34)$ |
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