Question

if x= 2+ root 3, find the value of x+1/x​

Answer 1

Answer:

hope it is help full

Step-by-step explanation:

x=2+√3

then,

1/x = 2-√3

there for

x+1/x = 2+√3+2-√3

x+1/x =4

Answer 2

Given:

$\star \: x = 2 + \sqrt{3}$

To find:

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

Solution:

$\implies \: x = 2 + \sqrt{3}$

Now , find 1/x

$\star \: \frac{1}{x} = \frac{1}{2 + \sqrt{3} }$

• Rationalise the denominator:

$\implies \: \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \\ \implies \: \frac{2 - \sqrt{3} }{ {2 }^{2} - { \sqrt{3} }^{2} } \\ \\ \implies \: \frac{2 - \sqrt{3} }{4 - 3} \\ \\ \implies \: 2 - \sqrt{3}$

Now,

$\star \: x + \frac{1}{x} \\ \\ \star \: 2 + \sqrt{3} + 2 - \sqrt{3} \\ \\ \star \: 4$