Question

X^2-b(x-1)-1=0 find. (x)

Answer 1

x^2 - b x + (b - 1) = 0

x = [ b +/- sqrt (b^2 - 4b+4 ) ]/2

Answer 2

just use the quadratic formula:

x^2 - bx + b-1 = 0
x = [b±√(b^2-4(b-1))]/2
= [b±√(b^2-4b+1)]/2

If you want an integer solution for b, then clearly b=2 and you have

x^2-2x+1 = (x-1)^2 = 0

For a real solution, you need
b^2-4b+1 >= 0
or b >= 2+√3

Not sure just where you want to go with this.

Answer 3

Hmmm. I seem to have disregarded the distributive property ...