Question

if x=√5+2 find x+1/x
i will mark brainliest​

Answer 1

Answer:

2√5

Step-by-step explanation:

x=√5+2

so 1/x=1/√5 + 2

rationalising this you will get

1/x=√5-2/(√5)²-2²

=√5-2/5-4

=√5-2

so, x + 1/x = √5 + 2 + √5 -2

                 =2√5

pls mark as brainliest

hope it helps

Answer 2

$\huge{\underline{\underline{\green{\sf{Given:}}}}}$

$\bf x = \sqrt{5}+2$

$\huge{\underline{\underline{\green{\sf{To\:\:Be\:\:Found:}}}}}$

$\bf Value\:\:of \:\:\bigg(x+\frac{1}{x} \bigg)$

Now,

We can get the value of $\bf \dfrac{1}{x}$.

$\bf x = \sqrt{5}+2\\ \\ So,\\ \\ \dfrac{1}{x} = \dfrac{1}{\sqrt{5}+2}$

Rationalising it.

$= \dfrac{1}{\sqrt{5}+2} \times \dfrac{\sqrt{5}-2}{\sqrt{5}-2}$

$= \dfrac{\sqrt{5}-2}{(\sqrt{5})^{2}-(2)^{2}} \:\:\bigg[ \therefore (a+b)(a-b)=(a)^2-(b)^2 \bigg]$

$= \dfrac{\sqrt{5}-2}{5-4} = \dfrac{\sqrt{5}-2}{1} = \sqrt{5}-2$

Now,

$\bf Value\:\:of \:\:\bigg(x+\frac{1}{x} \bigg) \\ \\ \\ = \sqrt{5} \: \cancel{+2} + \sqrt{5} \:\cancel{-2}\\ \\ \\ = 2 \sqrt{5}$

Hence,

$\red{\bf Value\:\:of \:\:\bigg(x+\frac{1}{x} \bigg) = \boxed{\boxed{2 \sqrt{5}}} }$