If the range of the function f(x)= 5-x x^2-3 x+2 , x 1,2 , is (- , ] [ , ) , then ^2+ ^2 is equal to :

Step-by-step solution

aligned & y= 5-x x^2-3 x+2 & y x^2-3 x y+2 y+x-5=0 & y z^2+(-3 y+1) x+(2 y-5)=0 aligned Case I : If y=0 (Accepted) x=5 Case II : If y 0 aligned & D 0 & (-3 y+1)^2-4(y)(2 y-5) 0 & 9 y^2+1-6 y-8 y^2+20 y 0 & y ^2+14 y+1 0 & (y+7)^2-48 0 & |y+7| 4 3 & y+7 4 3 or y +7 -4 3 & y 4 3 -7 or y -4 3 -7 aligned From Case I and Case II y (- ,-4 3 -7] [4 3 -7, ) So =-4 3 -7 =4 3 -7 aligned a^2+b^2 & =(-4 3 -7)^2+(4 3 -7)^2 & =2(48+49) & =194 aligned