If a-(1)/(a) =5 then what isa^(2)+(1)/(a^(2) )

Question

If
`a-(1)/(a) =5` then what is
`a^(2)+(1)/(a^(2) )`

Answer 1

Answer: 27

Work Shown:

`a - (1)/(a) = 5\\\\\left(a - (1)/(a)\right)^2 = 5^2\\\\\left(a\right)^2 - 2a*(1)/(a) + \left((1)/(a)\right)^2 = 25\\\\a^2 - 2 + (1)/(a^2) = 25\\\\a^2 + (1)/(a^2) = 25+2\\\\a^2 + (1)/(a^2) = 27\\\\`

Note: On the third step, I used the rule that
`(x-y)^2 = x^2-2xy+y^2`