Question

if X=1-✓2, find the value of (x-1/X)³​

Answer 1

Answer:

Step-by-step explanation:

Given, x = 1 - √2

1/x = 1 / 1 - √2=Rationalize the denominator, we get

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

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

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

= ( 1 + √2 ) / 1 - 2 ( ∵ square and root are cancelled )

= ( 1 + √2 ) / ( - 1 )

= ( - 1 - √2 )

( x - 1/x ) cube = [ 1 - √2 - ( - 1 - √2 ) ] cube

= [ 1 - √2 + 1 + √2 ] cube ( ∵ - × - = + )

= ( 1 + 1 - √2 + √2 ) cube

= ( 2 )cube ( ∵ - √2 + √2 = 0 )

= 8 ( ∵ 2 cube = 2 × 2 × 2 = 8 )

∴ ( x - 1/x ) cube = 8 is the answer.