The equation x+3−4x−1+x+8−6x−1=1  has

The given equation is x+3−4x−1+x+8−6x−1=1 Putx−1=t⇒x=t2+1 .The given equation becomest2+4−4t+t2+9−6t=1 ⇒ (t−2)2+(t−3)2=1 ⇒ |t−2|+|t−3|=1 ⇒ 2≤t≤3 ⇒ 2≤x−1≤3     (∵  t=x−1) ⇒ 4≤x−1≤9 ⇒ 5≤x≤10 .Hence the given equation is satisfied for all values of x  between 5  and10 .