Use the quadratic formula to solve the equation: x² - x - 1 = 0

Answer 1

A=1 b=-1 C=-1

b^2 - 4ac = (-1)^2 - 4(1)(-1) = 1 - 4(-1) = 1 + 4 = 5

x = (-(-1) + sqrt(5) ) / (2*1)

= (1 +or- sqrt(5))/2

check:

Let x = (1 +sqrt(5))/2 <--- the positive branch solution

Then x^2 = (1 + sqrt(5))^2/4 =

(1 + 2*sqrt(5) + 5)/4 =

(2 * sqrt(5) + 6)/4 =

(sqrt(5) + 3)/2

x^2 - x - 1 = (sqrt(5)+3)/2 - (1 + sqrt(5))/2 - 1

= 2/2 - 1 <--- there is negative sign in between so sqrt(5) cancels

= 1-1

= 0

therefore the solutions, appearing in bold above, are correct...