FRIENDS I DON'T KNOW WHAT THING THAT A GHOST AUR NOT OTHER THING BUT I AM NOT TELLING LIE I AM VERY SCARED. AND THANK TO GOD BECAUSE I AM NOW SAFE WHEN THAT GHOST OR WHAT IS THAT I DON'T KNOW BUT WHEN THAT THING IS COMING TO ME. JUST THAT TIME. MY MOTHER COME TO HOME. AND ALL LIGHTS ARE OFF BEFORE COMING MY MOTHER AT HOME AND WHEN MY MOTHER COME TO HOME SHE SWITCH ON THE LIGHTS AND THE GHOST OR ANYTHING THAT IS HAVE GO.
Answers
Answer:
\large\underline{\sf{Given- }}
Given−
\rm :\longmapsto\:n = 2 + \sqrt{3} :⟼n=2+
3
\large\underline{\sf{To\:Find - }}
ToFind−
\rm :\longmapsto\: {\bigg(n + \dfrac{1}{n} \bigg) }^{3} :⟼(n+
n
1
)
3
\large\underline{\sf{Solution-}}
Solution−
Given that
\rm :\longmapsto\:n = 2 + \sqrt{3} :⟼n=2+
3
Consider,
\bf :\longmapsto\:\dfrac{1}{n} :⟼
n
1
\rm \: = \: \:\dfrac{1}{2 + \sqrt{3} } =
2+
3
1
On rationalizing the denominator, we get
\rm \: = \: \:\dfrac{1}{2 + \sqrt{3} } \times \dfrac{2 - \sqrt{3} }{2 - \sqrt{3} } =
2+
3
1
×
2−
3
2−
3
\rm \: = \: \:\dfrac{2 - \sqrt{3} }{ {2}^{2} - {( \sqrt{3}) }^{2} } =
2
2
−(
3
)
2
2−
3
\: \: \: \: \: \: \red{\bigg \{ \because \:(x + y)(x - y) = {x}^{2} - {y}^{2} \bigg \}}{∵(x+y)(x−y)=x
2
−y
2
}
\rm \: = \: \:\dfrac{2 - \sqrt{3} }{4 - 3} =
4−3
2−
3
\rm \: = \: \:\dfrac{2 - \sqrt{3} }{1} =
1
2−
3
\rm \: = \: \:2 - \sqrt{3} =2−
3
\bf :\longmapsto\:\dfrac{1}{n} = 2 - \sqrt{3} :⟼
n
1
=2−
3
So,
\rm :\longmapsto\: \bigg(n + \dfrac{1}{n} \bigg)^{3} :⟼(n+
n
1
)
3
\rm \: = \: \: {\bigg(2 + \sqrt{3} + 2 - \sqrt{3} \bigg) }^{3} =(2+
3
+2−
3
)
3
\rm \: = \: \: {4}^{3} =4
3
\rm \: = \: \:64=64
Hence,
\bf :\longmapsto\: \bigg(n + \dfrac{1}{n} \bigg)^{3} = 64:⟼(n+
n
1
)
3
=64
Additional Information :-
More Identities to know:
↝(a + b)² = a² + 2ab + b²
↝(a - b)² = a² - 2ab + b²
↝a² - b² = (a + b)(a - b)
↝(a + b)² = (a - b)² + 4ab
↝(a - b)² = (a + b)² - 4ab
↝(a + b)² + (a - b)² = 2(a² + b²)
↝(a + b)³ = a³ + b³ + 3ab(a + b)
↝(a - b)³ = a³ - b³ - 3ab(a - b)
Answer:
It was not a ghost it is maybe someone's shadow or maybe it is yours .
Step-by-step explanation:
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