Question

%3A%20that%20%5C%3A%20%20%20%28a%20%2B%20%20%5Cfrac%7B1%7D%7Ba%7D%20%29%20%7B%7D%5E%7B2%7D%20%3D%2013%20" id="TexFormula1" title="if \: a \: - \frac{1}{a} = 3 \: prove \: that \: (a + \frac{1}{a} ) {}^{2} = 13 " alt="if \: a \: - \frac{1}{a} = 3 \: prove \: that \: (a + \frac{1}{a} ) {}^{2} = 13 " align="absmiddle" class="latex-formula">
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Answer 1

$\text{Given that ,}~~ \left(a - \dfrac 1a \right) =3\\\\\\ \text{We know that,} ~~4ab =(a+b)^2 -(a-b)^2\\\\\\4 \cdot a \cdot \dfrac 1a = \left(a + \dfrac 1a \right)^2 - \left(a - \dfrac 1a \right)^2\\\\\\\implies \left(a + \dfrac 1a \right)^2 = 4 + \left(a - \dfrac 1a \right)^2 = 4+3^2 = 4+9 =13\\\\\text{Proved}.$