[tex]x= \frac{-b +- \sqrt{b^2-4ac} }{2a} [/tex]
where ax² + bx + c = 0
For x² -nx + n²
a = 1
b = -n
c = n²
Substitute to formula:
[tex]x= \frac{n +- \sqrt{n^2-4(1)(n^2)} }{2(1)} [/tex]
[tex]x= \frac{n +- \sqrt{n^2-4n^2} }{2} [/tex]
[tex]x= \frac{n +- \sqrt{-3n^2} }{2} [/tex]
[tex]x= \frac{n +- n\sqrt{-3} }{2} [/tex]
[tex]\boxed{x_{1}= \frac{n +n\sqrt{-3} }{2}} [/tex]
[tex]\boxed{x_{2}= \frac{n -n\sqrt{-3} }{2}} [/tex]
