Question

a=√2+1 find the value of a^2+1/a^2+a+1/a-6​

Answer 1

Question:

a = √2 + 1 find the value of a^2 + 1/a^2 + a + 1/a - 6.

Given:

1. $a = \sqrt{2 + 1}$

To Find:

• Value of ${a}^{2} + \frac{1}{{a}^{2}} + a + \frac{1}{a} - 6$

Solution:

$\implies {(2 + 1)}^{2} + \frac{1}{ {(2 + 1)}^{2} } + (2 + 1) + \frac{1}{(2 + 1) } - 6$

$\implies \frac{ { \cancel {(2 + 1)}^{2}} + 1 }{\cancel{(2 + 1)}^{2} } + \frac{ \cancel{(2 + 1)} + 1 }{ \cancel{(2 + 1)}} - 6$

$\implies 1 + 1 - 6$

$\implies 2 - 6$

$\huge \boxed {\implies - 4}$