Difference between the corresponding roots of x2+ax+b=0 and x2+bx+a=0 is same and a≠b, then

Let α1, β1 are the roots of the equation x2+ax+b=0⇒x=-a±a2-4b2⇒α1=-a+a2-4b2, β1=-a-a2-4b2and α2, β2 are the roots of the equation x2+bx+a=0So, α2=-b+b2-4a2, β2=-b-b2-4a2Now α1-β1=a2-4b; α2-β2=b2-4aGiven, α1-β1=α2-β2⇒a2-4b=b2-4a⇒a2-b2=-4(a-b)⇒a+b+4=0