Question

if x =3+2root2 find the value of x^2+1/x^2
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Answer 1

Hi ,

x = 3 + 2√2 ---( 1 )

1/x = 1/( 3 + 2√2 )

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

= ( 3 - 2√2 )/ [ 3² - ( 2√2 )² ]

= ( 3 - 2√2 ) / ( 9 - 8 )

= 3 - 2√2 ----( 2 )

x + 1/x = 3 + 2√2 + 3 - 2√2

= 6 ----( 3 )

Now ,

do the Square of equation ( 3 ) , we get

( x + 1/x )² = 6²

x² + 1/x² + 2 = 36

x² + 1/x² = 36 - 2

= 34

I hope this helps you.

: )

Answer 2

Answer:

34

Step-by-step explanation:

X=3+2√2

1/x=1/(3+2√2)

=3-2√2/{(3+2√2)(3-2√2)} .....(rationalizing the irrational number in the denominator)

= 3-2√2/(9-8) ....[(a+b)(a-b)=a^2+b^2]

=3-2√2

X+1/x=3+2√2+3-2√2

=6

(X+1/x)² =6²

X² +1/x² +2=36

X² +1/x² =34

Hope this answer helps

;-) -_-