# How do you solve the quadratic #u^2-2u+3=0# using any method?

##### 1 Answer

Sep 26, 2016

#### Answer:

#### Explanation:

The difference of squares identity can be written:

#a^2-b^2 = (a-b)(a+b)#

Use this with

#0 = u^2-2u+3#

#color(white)(0) = u^2-2u+1+2#

#color(white)(0) = (u-1)^2-(sqrt(2)i)^2#

#color(white)(0) = ((u-1)-sqrt(2)i)((u-1)+sqrt(2)i)#

#color(white)(0) = (u-1-sqrt(2)i)(u-1+sqrt(2)i)#

Hence