How will this be solved a^4 + 20^2 - 576. A bit explanation on how to solve questions like this. The clue behind this. Thanks

Question

quadratic equations

Answer 1

I think you mean a^4+20a^2-576 as the expression.

This is a quadratic in a^2: (a^2)^2+20(a^2)-576, treating a^2 like a single variable.

We're looking for factors of 576 whose difference is 20. The factors are 16 and 36.

This takes us to the next stage: (a^2-16)(a^2+36),

If we for the moment discount complex numbers, we can factorise further:

(a-4)(a+4)(a^2+36). This gives us two zeroes, 4 and -4.

The other two are complex: (a-6i)(a+6i) where i=√-1. So a=6i and -6i.

Complete factorisation is (a-4)(a+4)(a-6i)(a+6i).

Answer 2

How will this be solved a^4 + 20^2 - 576. A bit explanation on how to solve questions like this. The clue behind this. Thanks

This is just a quaderatic equation, in a^2.

substitute u = a^2 in your equation, to get

u^2 + 20u - 576 = 0

This factorises as,

(u + 36)(u - 16) = 0, then

u = -36 , u = 16

if we are only asked for real solutions, and since u must be positive (u = a^2) then we ignore the negative solution and we end up with only

u = 16

i.e. a^2 = 16

Therefore, a = -4, a = +4