Question

X² - 6x + 4 = 0

solve and show work. ...?

Answer 1

The answer is 3 + √5 and 3 - √5.

This is quadratic equation: x² - 6x + 4 = 0
The general quadratic equation is ax² + bx + c = 0
Our equation can be rewritten: 1x² + (-6)x + 4 = 0
So, in our equation we have: a = 1, b = -6, c = 4

Now, x can be calculated using the formula:
`x_(1,2)= \frac{-b+/- \sqrt{ b^(2)-4ac } }{2a}`

`x_(1,2) =\frac{-(-6)+/- \sqrt{ (-6)^(2)-4*1*4 } }{2*1} = (6+/- √(36-16) )/(2) = (6+/- √(20) )/(2) =(6+/- √(4*5) )/(2)= \\ =(6+/- √(4)* √(5) )/(2) =(2*3+/- 2√(5) )/(2)= (2(3+/- √(5)) )/(2) =3+/- √(5)`

From here:

`x_(1) =3+ √(5) \\ x_(2) =3- √(5)`