Question

if a= V2 +1, find value of:
(i) a+1/a
(ii) a -1/a​

Answer 1

(i) 2√2

(ii) 2

Step-by-step explanation:

$a = \sqrt{2} + 1$

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

$\frac{1}{a} = \frac{1}{ \sqrt{2} + 1 } \times \frac{ \sqrt{2} - 1 }{ \sqrt{2} - 1 }$

$\frac{1}{a} = \frac{ \sqrt{2} - 1}{2 - 1}$

$\frac{1}{a} = \sqrt{2} - 1$

(i) a+ 1/a

√2+1+√2-1

=2√2

(ii) a - 1/a

√2+1-(√2-1)

=√2+1-√2+1

=2