If $ x = {\sqrt\frac{2+{\sqrt3}}{2 -{\sqrt3}}}$, then determine the value of $X^2 + x – 9 ?$
If $ x = {\sqrt\frac{2+{\sqrt3}}{2 -{\sqrt3}}}$, then determine the value of $x^2 + x – 9 ?$
$ x = {\sqrt\frac{2+{\sqrt3}}{2 -{\sqrt3}}}$,फिर का मान निर्धारित करें $ x^2 + x – 9 ? $
Detailed Solution & Logic
Correct Answer:
$5\sqrt{3}$
Solution:
Given:
$x=\sqrt{\frac{2+\sqrt3}{2-\sqrt3}}$
Rationalizing:
$x=\sqrt{(2+\sqrt3)^2}$
$x=2+\sqrt3$
Now,
$x^2+x-9$
$=(2+\sqrt3)^2+(2+\sqrt3)-9$
$=7+4\sqrt3+2+\sqrt3-9$
$=5\sqrt3$
Answer: $5\sqrt3$
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