Question

if a = 3 - 2√2, find the value of a² - 1 / a²​

Answer 1

$\huge\sf\color{red}{Here\:It\:Goes}$ $\huge\large\downarrow{}$

$\begin{gathered}a = 3 - 2 \sqrt{2} \\ \frac{1}{a} = \frac{1}{3 - 2 \sqrt{2} } = \frac{3 + 2 \sqrt{2} }{(3 + 2 \sqrt{2} )(3 - 2 \sqrt{2} )} \\ \frac{1}{a} = \frac{3 + 2 \sqrt{2} }{9 - 8} = 3 + 2 \sqrt{2} \\ \\ now. \: a + \frac{1}{a} = 3 - 2 \sqrt{2} + 3 + 2 \sqrt{2} = 6 \\ \\ a - \frac{1}{a} = 3 - 2 \sqrt{2} - 3 - 2 \sqrt{2} = - 4 \sqrt{2} \\ \\ thus \: \: \: {a}^{2} - \frac{1}{ {a}^{2} } = (a + \frac{1}{a} )(a - \frac{1}{a} ) \\ = 6 \times ( - 4 \sqrt{2}) = - 24 \sqrt{2} \end{gathered}$

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