Question

if x=1-√2 find the value of (x-1/x)cube

Answer 1

x=1-√21+√2
1/x= 1/(1-√2)
= (1+√2)/(1-√2)(1+√2)
=(1+√2)/(1^2-√2^2)
=(1+√2)/(1 -2)
=(1+√2)/-1
=-(1+√2)
therefore x-1/x= (1-√2)-{-(1+√2)}
=1-√2+1+√2
=2
therefore x-1/x= 2^3= 8
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Answer 2

if x = 1 - √2 , then ( x - 1 / x )^3 = ?
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step 1 Find 1 / x :
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1 / x = 1 /( 1 - √2 )

by rationalizing denominator , we get

= 1 / ( 1 - √2 ) × (1 + √2 ) /( 1 + √2 )

=( 1 + √2 ) / 1 - 2 = - ( 1 + √2 )

so now ,

x - 1 / x = ( 1 - √2 ) - { - ( 1 + √2 ) }

x - 1 / x = 1 - √2 - ( -1 - √2 )

x - 1 / x = 1 - √2 + 1 + √2

x - 1 / x = 2 _______________________________

by taking cube both side , we get

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

( x - 1 / x )^3 = 8

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Your Answer = 8
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