Work Shown:
[tex]a - \frac{1}{a} = 5\\\\\left(a - \frac{1}{a}\right)^2 = 5^2\\\\\left(a\right)^2 - 2a*\frac{1}{a} + \left(\frac{1}{a}\right)^2 = 25\\\\a^2 - 2 + \frac{1}{a^2} = 25\\\\a^2 + \frac{1}{a^2} = 25+2\\\\a^2 + \frac{1}{a^2} = 27\\\\[/tex]
Note: On the third step, I used the rule that [tex](x-y)^2 = x^2-2xy+y^2[/tex]
