If b>a, then the equation (x-a)(x-b)=1 has

The equation is x2-(a+b)x+ab-1=0∴ discriminant =(a+b)2-4(ab-1)=(b-a)2+4>0∴ both roots are real. Let them be α,β whereα=(a+b)-(b-)2+42, β=(a+b)+(b-a)2+42Clearly, α<(a+b)-(b-a)22=(a+b)-(b-a)2=a(∵b>a)and β>(a+b)+(b-a)22=a+b+b-a2=bHence, one root α is less than a and the other root β is greater than b.