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

1 Answer
George C.
Sep 26, 2016

u = 1+-sqrt(2)i

Explanation:

The difference of squares identity can be written:

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

Use this with a=(u-1) and b=sqrt(2)i as follows:

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 u = 1+-sqrt(2)i

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