If x is rea, then the maximum and minimum values of expression x2+14x+9x2+2x+3 will be

Let y=x2+14x+9x2+2x+3⇒y(x2+2x+3)-x2-14x-9=0⇒(y-1)x2+(2y-14)x+3y-9=0For real x, its discriminant ≥0i.e. 4(y-7)2-4(y-1)3(y-3)≥0⇒y2+y-20≤0 or (y-4)(y+5)≤0Now, the product of two factors is negative if these are of opposite signs. So following two cases arise:Case I: y-4≥0 or y≥4 and y+5≤0 or y≤-5This is not possible.Case II: y-4≤0 or y≤4 and y+5≥0 or y≥-5Both of these are satisfied if -5≤y≤4Hence maximum value of y is 4 and minimum value is -5.