Question

If x = 7 + 4 √3 , then x + 1/x is equal to
10
12
14
16​

Answer 1

$\large\bold{\underline{\underline{Given:-}}}$

$x = 7 + 4 \sqrt{3}$

$\large\bold{\underline{\underline{To\:find:-}}}$

$x + \frac{1}{x}$

$\large\bold{\underline{\underline{Solution:-}}}$

$\boxed{ (c) \:14 }$ ☑

$\large\bold{\underline{\underline{Step-by-step\:explanation:-}}}$

Let us first solve for $\frac{1}{x}$.

We have,

$:⟼  \frac{1}{7 + 4 \sqrt{3} }$

$:⟼   \frac{1}{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} }$

$:⟼   \frac{1(7 - 4 \sqrt{3}) }{ ({7})^{2} - ( {4 \sqrt{3} })^{2} }$

$:⟼   \frac{7 - 4 \sqrt{3} }{49 - 48}$

$:⟼   \frac{7 - 4 \sqrt{3} }{1}$

$:⟼  7 - 4 \sqrt{3}$

Now,

$:⟼  x + \frac{1}{x}$

$:⟼  7 + 4 \sqrt{3} + 7 - 4 \sqrt{3}$

$:⟼  7 + 7$

$:⟼  14$

Note:

$↬(a + b)(a - b) = {a}^{2} - {b}^{2}$

$\sf\red{Hope\:it\:helps.}$