Question

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

Answer 1

Step-by-step explanation:

given: x= 1-√2

need to solve: (x-1/x)^3

firstly, by substituting the x value in given expression....

so, ( 1-√2) -(1)/(1-√2)

by taking LCM: LCM= 1-√2

= (1-√2)(1-√2)-1/1-√2

= (1-√2)^2-1/1-√2

= 1+2-2√2-1/1-√2

= 2-2√2/1-√2

now, by applying whole cube on the above expression...

so, (2-2√2)^3/(1-√2)^3

(a-b)^3= a^3-b^3-3ab(a-b): formula

so, 4-16√2-12√2(2-2√2)/1-2√2-3√2(1-√2)

= 4-16√2-24√2+48/1-2√2-3√2+6

= 52-40√2/7-5√2

so, answer= 52-40√2/7-5√2

hope it helps you!