solve x^6 - 64 = 0
5 answers
(x+2)(x^2-2x+4)(x-2)(x^2+2x+4)
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
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)
x+8<4 help me self this please,
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