Question

If x=7-4√3 find the value of x square- 1/ x square

Answer 1

Solution

$x = 7 - 4 \sqrt{3} \\ = > \frac{1}{x} = \frac{1}{7 - 4 \sqrt{3} } \\ = > \frac{1}{x} = \frac{7 + 4 \sqrt{3} }{(7 - 4 \sqrt{3})(7 + 4 \sqrt{3} )} \\ = > \frac{1}{x} = \frac{7 + 4 \sqrt{3} }{49 - 48} = 7 + 4 \sqrt{3} \\ now....... \\ x + \frac{1}{x} = 7 - 4 \sqrt{3} + 7 + 4 \sqrt{3} = 14 \\ and \\x - \frac{1}{x} = 7 - 4 \sqrt{3} - 7 - 4 \sqrt{3} = - 8 \sqrt{3}$

now...

$x {}^{2} - \frac{1}{x {}^{2} } \\ = (x + \frac{1}{x} )(x - \frac{1}{x} ) \\ = 14 (- 8 \sqrt{3} ) \\ = - 112 \sqrt{3}$

hope this helps you....