Question

`if \: a \: - (1)/(a) = 3 \: prove \: that \: (a + (1)/(a) ) {}^(2) = 13`

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Answer 1

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