Question

Hey

If x = 1 + √2 , find x² + 1/x² ​

Answer 1

$\huge{\color{red}{\fbox{\textsf{\textbf{HeY⛄}}}}}$

Here , x = 1 + √2

So x^2 = ( 1 + √2) ^2

x^2 = 1² + 2×1× √2 + (√2)^2

[ Taking Identity = ( a+b)² = a² + 2ab + b² ]

x^2 = 3+ 2 √2

We get x^2 ( x²) = 3+ 2 √2

So 1/x² = 1/3+ 2 √2

So values of x² + 1/x²

3+ 2 √2 + 1/ 3+ 2 √2

( 3+ 2 √2 )² + 1 / 3+ 2 √2

= 9+ 2×3× 2√2 + 8 + 1 / 3+ 2 √2

[ Taking Identity = ( a+b)² = a² + 2ab + b² ]

= 18 + 12√2 / 3+ 2 √2

= 6( 3+ 2√2 ) / 3+ 2 √2

= 6

( SEE the attachment also if you have any doubt regarding this )

:)

Answer 2

Answer:

Here , x = 1 + √2

So x^2 = ( 1 + √2) ^2

x^2 = 1² + 2×1× √2 + (√2)^2

[ Taking Identity = ( a+b)² = a² + 2ab + b² ]

x^2 = 3+ 2 √2

We get x^2 ( x²) = 3+ 2 √2

So 1/x² = 1/3+ 2 √2

So values of x² + 1/x²

3+ 2 √2 + 1/ 3+ 2 √2

( 3+ 2 √2 )² + 1 / 3+ 2 √2

= 9+ 2×3× 2√2 + 8 + 1 / 3+ 2 √2

[ Taking Identity = ( a+b)² = a² + 2ab + b² ]

= 18 + 12√2 / 3+ 2 √2

= 6( 3+ 2√2 ) / 3+ 2 √2

= 6

( SEE the attachment also if you have any doubt regarding this )

:)