The sum of all real roots of the equation | x -3|^2+| x -3|-2=0 is

Step-by-step solution

aligned & | x -3|^2+| x -3|-2=0 & Let | x -3|= t & t ^2+ t -2=0 t ^2+2 t - t -2=0 aligned aligned & t ( t +2)-1( t +2)=0 & ( t +2)( t -1)=0 & t =-2 or t =1 aligned Since t is modulus of a number, it cannot be negative. aligned & t =1 | x -3|=1 x -3=1 or x -3=-1 & x =4 or 2 aligned Sum of roots =4+2=6 .