Question

if a = √2+1, find the value of (a-1/a​)^2

Answer 1

Answer:

Step-by-step explanation:

A=√2+1

1/A=1/(√2+1)

By rationalising

1/(√2+1) *(√2-1)/(√2-1)

(√2-1)/(√2^2-1^2)

√2-1/(2-1)

√2-1

Answer 2

Answer:

SOLUTION

a=√2+1

1/a=1/(√2+1 )

=

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

${ (a - \frac{1}{a} ) }^{2} = {(\sqrt{2} + 1 - ( \sqrt{2} - 1 ) )}^{2} = {( \sqrt{2} + 1 - \sqrt{2} + 1 })^{2} = {(1 + 1)}^{2} = {2}^{2} = 4$HOPE IT HELPS

THEANSWER IS 4