Question

x = (7+4√3) find x + 1/x

Answer 1

x = 7+4√3
so, 1/x = 1/7+4√3
= 1(7-4√3) / (7+4√3)(7-4√3)
(multiplying numerator and denominator by (7-4√3)
=7-4√3 / 7^2 - (4√3)^2 (a^2-b^2 = (a+b)(a-b)
=7-4√3 / 49 - 48
= 7 - 4√3 /1
=7 - 4√3
so, x + 1/x
= 7 + 4√3 + (7 - 4√3)
= 7 + 4√3 + 7 + (- 4√3)
= 14

Answer 2

Hey there !

Thanks for the Question !

Here's the answer !

Given that, x = ${7 + 4\sqrt{3}$

To Find : $x + \frac{1}{x} = ?$

Proof:

$\frac{1}{x} = \frac{1}{7 + 4 \sqrt{3} } \\\\ Rationalising \ the \ denominator \ we \ get, \\\\ \frac{1}{7 + 4 \sqrt{3} } \times \frac{ 7 - 4 \sqrt{3}}{7 - 4 \sqrt{3} } \\\\\\ => \frac{ 7 - 4 \sqrt{3} }{ 7^2 - ( 4 \sqrt{3} )^2} \\\\\\ => \frac{7 - 4 \sqrt{3} }{ 49 - 48 } \\\\ => \frac{7 - 4 \sqrt{3} }{1} = 7 - 4 \sqrt{3} \\\\ => \frac{1}{x} = 7 - 4 \sqrt{3} \\\\ => x + \frac{1}{x} = 7 + 4 \sqrt{3} + 7 - 4 \sqrt{3} \\\\ => x + \frac{1}{x} = 14$

This is the final solution.

Hope my answer helped !