The sum of the squares of the roots of | x +2|^2+| x -2|-2=0 and the squares of the roots of x^2-2|x-3|-5=0 , is

Step-by-step solution

aligned & | x -2|^2+2| x -2|-| x -2|-2=0 & (| x -2|+2)(| x -2|-1)=0 & | x -2|=1 & x =2 1=3,1 & sum of square of roots =9+1=10 & x ^2-2| x -3|-5=0 & Case-I x -3 0 & x ^2-2 x +1=0 & ( x -1)^2=0 & x =1 aligned But x 3 x Case-II x -3 0 x^2+2 x-11=0, D 0 Real & distinct roots f(x)=x^2+2 x-11 f (3) 0, - p 2 a =-1 3 both roots 3 , both roots acceptable Sum of square of roots =( + )^2-2 aligned & =4+22=26 & Final sum =10+26=36 aligned