Question

if a=4/7+√3 find a²-1/a

Answer 1

$a = \frac{4}{7 + \sqrt{3} } \\ rationalise \: the \: denominator \\ a = \frac{4}{7 + \sqrt{3} } \times \frac{7 - \sqrt{3} }{7 - \sqrt{3} } \\ = \frac{28 - 4 \sqrt{3} }{49 - 3} \\ = \frac{28 - 4 \sqrt{3} }{46} \\ = \frac{16 - 2 \sqrt{3} }{23} \\ {a}^{2} - \frac{1}{a} = (256 + 12 - 64 \sqrt{3} ) \div 529 - \frac{7 + \sqrt{3} }{4} \\ = \frac{268 - 64 \sqrt{3} }{529} - \frac{7 + \sqrt{3} }{4}$
it is going to be too tough ahead.is it confirm a^2