Question

If = 5+root 6 then x + 1 / 2
B) 89
A)
()98
D) 100​

Answer 1

Answer:

I thought D is the currect answer

Answer 2

$x = 5 + \sqrt{6}$

And,

$x + \frac{1}{2} \\ \\ = > 5 + \sqrt{6} + \frac{1}{2} \\ \\ = > \frac{10 + 2 \sqrt{6} + 1 }{2} = \frac{11 + 2 \sqrt{6} }{2} \\ \\ = > \frac{11}{2} + \frac{2 \sqrt{6} }{2} = 5.5 + \sqrt{6}$

Or,

Given,

$x = 5 + \sqrt{6}$

And,

$\frac{1}{x} = \frac{1}{5 + \sqrt{6} } \times \frac{5 - \sqrt{6} }{5 - \sqrt{6} } \\ \\ = > \frac{5 - \sqrt{6} }{25 - 6} = \frac{5 - \sqrt{6} }{19}$

Now,

$x + \frac{1}{x} = > 5 + \sqrt{6} + \frac{5 - \sqrt{6} }{19} \\ \\ = > \frac{19(5 + \sqrt{6}) + 5 - \sqrt{6} }{19} \\ \\ = > \frac{95 + 19 \sqrt{6} + 5 - \sqrt{6} }{19} \\ \\ = > \frac{100 + 18 \sqrt{6} }{19}$