Question

if a=4/7+√3 find a²-1/a

Answer 1

$a = \frac{4}{7 + \sqrt{3} } \\ {a} = \frac{4}{7 + \sqrt{3} } \times \frac{7 - \sqrt{3} }{7 - \sqrt{3} } \\ a = \frac{28 - 4 \sqrt{3} }{49 - 3} \\ a = \frac{28 - 4 \sqrt{3} }{46} \\ a = \frac{14 - 2 \sqrt{3} }{23} \\ {a}^{2} = \frac{196 + 12 - 56 \sqrt{3} }{529} \\ = \frac{208 - 56 \sqrt{3} }{529} \\ {a}^{2} - \frac{1}{a} = \frac{208 - 56 \sqrt{3} }{529} - \frac{7 + \sqrt{3} }{4}$
this calculation goes too tough ahead,i think there are some problem in the question