Question

if (x-1/x)^3=8 then( x+1/x)=?

Answer 1

(x-1/x)^3=8

;x-1/x=3√8=2

again
(x-1/x)^2=x^2+1/x^2-2x×1/x

;2^2=x^2+1/x^3-2

;4+2=x^2+1/x^2
x^2+1/x^2=6...... eq (1)

again
(x+1/x)^2=x^2+1/x^2+2x×1/x

;(x+1/x)^2=6+2

;x+1/x=√8

;x+1/x=2√2

is your answer

Answer 2

Given inequality is

∣x−1∣+∣x−3∣≤8

Case I  x<1

∣x−1∣+∣x−3∣≤8

⇒−(x−1)−(x−3)≤8

⇒−2x+4≤8

⇒−2x≤4⇒x≥−2

Interval [−2,1)

Case II 1≤x<3

⇒x−1−x+3≤8⇒2≤8

Interval [1,3]

Case III x≥3

⇒x−1+x−3≤8⇒x≤6

Interval [3,6]

From all the interval

values of x lie in the interval [−2,6]