Question

if x=3-2√2 then find the value of [x^2-1/x^2​

Answer 1

Given,

x = 3 - 2√2

Find the value of -

${x}^{2}$- 1 / ${x}^{2}$

Given is the value of x..

So firstly we will find 1/x..

1/x = 1/3-2√2

Rationalizing the denominator,

= (1/ 3 - 2√2)×(3 + 2√2 / 3 - 2√2)

= 3 + 2√2 / ${3}^{2}$ - (2√2)^2

= 3 + 2√2 / 9 - 8

= 3 + 2√2 / 1

= 3 + 2√2

${x}^{2}$ - 1/${x}^{2}$ =

(3 - 2√2)^2 - (3 + 2√2)^2

= ${3}^{2}$ - (2√2)^2 + 2 × 3 × 2√2 - [${3}^{2}$ + (2√2)^2 + 2 × 3 × 2√2]

= 9 - 8 + 12√2 - (9 + 8 + 12√2)

= 9 - 8 + 12√2 - 9 - 8 - 12√2

= -16

Answer 2

Answer:

Step-by-step explanation:

Given,

x = 3 - 2√2

Find the value of -

- 1 /

Given is the value of x..

So firstly we will find 1/x..

1/x = 1/3-2√2

Rationalizing the denominator,

= (1/ 3 - 2√2)×(3 + 2√2 / 3 - 2√2)

= 3 + 2√2 / - (2√2)^2

= 3 + 2√2 / 9 - 8

= 3 + 2√2 / 1

= 3 + 2√2

- 1/ =

(3 - 2√2)^2 - (3 + 2√2)^2

= - (2√2)^2 + 2 × 3 × 2√2 - [ + (2√2)^2 + 2 × 3 × 2√2]

= 9 - 8 + 12√2 - (9 + 8 + 12√2)

= 9 - 8 + 12√2 - 9 - 8 - 12√2

= -16