college algebra

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solve x^6 - 64 = 0

• college algebra - ,

(x+2)(x^2-2x+4)(x-2)(x^2+2x+4)

• college algebra - ,

x ^ 6 - 64 = 0 Add 64 to both sides

x ^ 6 - 64 + 64 = 0 + 64

x ^ 6 = 64

x = sixth root of 64

x = + OR - 2

Solutions :

x = - 2

and

x = 2

• college algebra - ,

since you have a x^6 .... there will be 6 solutions including complex numbers.

Bosnian gave you the two real roots,
Monic only factored the expression, using the factored form we can find the 4 complex roots

x^2 - 2x + 4 = 0
x^2 - 2x + 1 = -4+1
(x-1)^2 = -3
x-1 = ±√3 i
x = 1 ± √3 i

In a similar way
x^2 + 2x + 4 = 0 gives us
x = -1 ±√3 i

(when solving quadratics with a coefficient of 1 for the x^2 term and an EVEN middle coefficient, I always use completing the square rather than the formula, it is faster and yields the answer in reduced form)

• college algebra - ,

x+8<4 help me self this please,

• college algebra - ,

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