Question

if x=1+√2
find the value of (x-1/x) ³
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Answer 1

Answer :

(x - 1/x)³ = 8

Solution :

• Given : x = 1 + √2
• To find : (x - 1/x)³ = ?

We have ;

x = 1 + √2

Thus ,

=> 1/x = 1/(1 + √2)

=> 1/x = 1/(√2 + 1)

Now ,

Rationalising the denominator of the term in RHS , we have ;

=> 1/x = (√2 - 1)/(√2 + 1)(√2 - 1)

=> 1/x = (√2 - 1) / [ (√2)² - 1² ]

=> 1/x = (√2 - 1)/(2 - 1)

=> 1/x = (√2 - 1)/1

=> 1/x = √2 - 1

Now ,

=> (x - 1/x)³ = [ (√2 + 1) - (√2 - 1) ]³

=> (x - 1/x)³ = (√2 + 1 - √2 + 1)³

=> (x - 1/x)³ = 2³

=> (x - 1/x)³ = 8

Hence , (x - 1/x)³ = 8 .