sum of squares

[teddy7]

The question I'm trying to solve is:
Factor a sum of squares, x² + a². What do you conclude?

I found this: Sum of squares: a^{[SIZE=-1]2[/SIZE]} + b^{[SIZE=-1]2[/SIZE]} = (a – bi)(a + bi) Note: a^{[SIZE=-1]2[/SIZE]} + b^{[SIZE=-1]2[/SIZE]} does not factor using real numbers.


So I just have no idea how to show my work for this question, if anyone could help me out that would be great! Thanks

 

[stapel]

The question I'm trying to solve is:
Factor a sum of squares, x² + a². What do you conclude?

If you're working within a context which does not have complex numbers, then I have no idea what they're wanting. If you are, then all one can "conclude", I suppose, is that one needs complex numbers for factoring sums of squares.

But I really don't know what they're expecting. The question is much too vague.

 

[Dale10101]

Maybe

The question I'm trying to solve is:
Factor a sum of squares, x² + a². What do you conclude?

I found this: Sum of squares: a^{[SIZE=-1]2[/SIZE]} + b^{[SIZE=-1]2[/SIZE]} = (a – bi)(a + bi) Note: a^{[SIZE=-1]2[/SIZE]} + b^{[SIZE=-1]2[/SIZE]} does not factor using real numbers.


So I just have no idea how to show my work for this question, if anyone could help me out that would be great! Thanks

Please double click on the image and then double click again to enlarge.

 

[Bob Brown MSEE]

Sum of squares: a^{[SIZE=-1]2[/SIZE]} + b^{[SIZE=-1]2[/SIZE]} = (a – bi)(a + bi) Note: a^{[SIZE=-1]2[/SIZE]} + b^{[SIZE=-1]2[/SIZE]} does not factor using real numbers.

This is perfect

 

[Bob Brown MSEE]

Just thinking aloud.
x^2+ y^2 is a quadratic polynomial.


The big gun is quad formula
x^2+ y^2 = 0
a=1
b=0
c=y^2

Roots: (+yi, -yi)
so x^2+ y^2 = (x+yi)(x-yi)

 

[Dale10101]

OK

Just thinking aloud.
x^2+ y^2 is a quadratic polynomial.


The big gun is quad formula
x^2+ y^2 = 0
a=1
b=0
c=y^2

Roots: (+yi, -yi)
so x^2+ y^2 = (x+yi)(x-yi)

Danke