Posted by **jerroyle** on Friday, August 23, 2013 at 9:28am.

what is the factor of a^4-7a^2+9 ?

- math -
**Steve**, Friday, August 23, 2013 at 12:39pm
a^4-7a^2+9

a^2 = (7±√13)/2

Now it gets tricky:

7+√13 = (1+2√13+13)/2 = (1+√13)^2/2

So, if

a^2 = (7+√13)/2 = (1+√13)^2/4

a = ±1/2 (√13+1)

and

a = ±1/2 (√13-1)

Makes things kind of nasty, the factors are

1/16 (±2x + √13 ± 1)

where all 4 combinations of + and - are used.

- math -
**MathMate**, Friday, August 23, 2013 at 12:40pm
Hint:

substitute u=a^2, then

a^4-7a^2+9

=u^2-7u+9

and try to factorize.

However, check you question to see if there is a typo. The above expression in u does not have rational factors.

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