If _ x 1 x^2- a x+ b x-1 =7 , then a + b is equal to

Step-by-step solution

_ x 1 x^2-a x+b x-1 =7 Limit exists if x^2- a x+ b at x=1 is 0 . array ll & (1)^2- a + b =0 & 1- a + b =0 a - b =1 ...(i) & _ x 1 x^2-(1+ b ) x+ b x-1 =7 & _ x 1 x^2-x- b x+ b x-1 =7 array aligned & _ x 1 (x-1)(x-b) x-1 =7 & 1- b =7 & [x 1, x 1, x-1 0] & b =-6 aligned From (i) a=-5 a+b=-5-6=-11