Question

x= 1 + root 2 then find (x-1/x)^3

Answer 1

Heya ✋

Let see your answer !!!!!!

Given that

x = 1 + √2

(x - 1/x)^3 = ?

Solution

1/x = 1/1 + √2

= 1 × (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

Hence ,

(x - 1/x)^3

= (2)^3

= 8






Thanks :))))

Answer 2

Hey !
Here is your answer !!

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Given !!
x = 1 + √2 , 
Solution ---
1/x = 1 / (√2 + 1) 
Rationalise the denominator !!!
　= (√2 - 1) / (√2 + 1)(√2 - 1) 

　= (√2 - 1) / (2 - 1) 

　= √2 - 1 

x - 1/x = (1 + √2) - (√2 - 1) = 2 

Then (x - 1/x)³ = 8 
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Hope it helps ☺