Question

If $x=\sqrt{\frac{7+4\sqrt{3}}{7-4\sqrt{3}}}$, then $x^2{(x-14)}^2=$........

• A. $1$
• B. $-1$
• C. $2$
• D. $-2$

Answer 1

The correct option is A $1$

multiply the numerator and denominator by

$\Rightarrow x=\sqrt{\frac{(7+4\sqrt{3}{)}^2}{1}}$ multiply the numerator and denominator by $(7+4\sqrt{3})$

$\therefore x^2(x-14{)}^2=(7+4\sqrt{3}{)}^2{[7+4\sqrt{3}-14]}^2$

$={\left[\right(7+4\sqrt{3}\left)\right(4\sqrt{3}-7\left)\right]}^2$

$=(-1{)}^2=1$