Question

If x = 3 – 2 underoot 2, find (i) x² +1/x^2

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Answer 1

Answer:

x= 3 - 2v2 ---(1)

1/x = 1/( 3 - 2v2 )

= ( 3 + 2v2 )/[(3 - 2v2 )(3+2/2 )]

= (3+ 2v2 )/[3? - (2v2 )2]

= (3+2v2)/(9 - 8)

= 3 + 2v2 ----( 2)

x + 1/x = 3 - 2v2 + 3 + 2v2

--(3)

X - 1/x = 3 - 2v2 - (3 + 2v2)

= 3 - 2v2 - 3 - 2V2

--- (4) = - 4V2 ---

Now,

x? - 1/x? = ( x + 1/x ) (x - 1/x )

= 6 x (- 4v2 )

[ From (3) and ( 4 )]

= - 24v2

Answer 2

Answer:

34

Step-by-step explanation:

( i)

$x =3 -2 \sqrt{2} \\ \frac{1}{x} = \frac{1}{3 - 2 \sqrt{2} } \\ \frac{1}{x} = \frac{1( \:3 + 2 \sqrt{2})}{3 - 2 \sqrt{2}( \:3 + 2 \sqrt{2}) } \\ \frac{1}{x} = 3 + 2 \sqrt{2}$

${x}^{2} + \frac{1}{{x}^{2} } = {(x + \frac{1}{x} )}^{2} - 2 \\ = { \: (3 + 2 \sqrt{2} + 3 - 2 \sqrt{2} ) }^{2} - 2 \\ = {6}^{2} - 2 \\ = 36 - 2 \\ = 34$