Kuldeepak Dhar Dwivedi
Last Activity: 3 Years ago
let y=1/(x²-x-1)
=>yx²-yx-y=1
=>yx²-yc-y-1=0
now
if y is not equal to zero:
as x is real thus determinant of the function in terms of x must be greater than 0,
thus y²-4(y)(-y-1)≥0
=>y(y-4(-y-1))≥0
=>Y(5y+4)≥0
=> Y belongs to (-infinity,-4/5]u(0, infinity)
Y=0 is not possible as for that denominator must be infinity but that will make the equation undefined
thus, its range is (-infinity,-4/5]u(0, infinity)
