Asked by Martha
solve x^6 - 64 = 0
Answers
Answered by
monic
(x+2)(x^2-2x+4)(x-2)(x^2+2x+4)
Answered by
Bosnian
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
x ^ 6 - 64 + 64 = 0 + 64
x ^ 6 = 64
x = sixth root of 64
x = + OR - 2
Solutions :
x = - 2
and
x = 2
Answered by
Reiny
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)
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)
Answered by
Sue
x+8<4 help me self this please,
Answered by
Ebony
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