SOLUTION: please help me solve this equation {{{ 8x^3-1=0 }}}

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Question 355697: please help me solve this equation +8x%5E3-1=0+
Found 3 solutions by Fombitz, Theo, ewatrrr:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
It's the difference of two cubes and can be factored.
8x%5E3-1=%282x-1%29%284x%5E2%2B2x%2B1%29=0
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Real solution:
2x-1=0
2x=1
highlight%28x=1%2F2%29
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.
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Complex solution:
4x%5E2%2B2x%2B1=0
Use the quadratic formula,
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-2%2B-+sqrt%28+2%5E2-4%2A4%2A1+%29%29%2F%282%2A4%29+
x+=+%28-2%2B-+sqrt%28+4-16+%29%29%2F8+
x+=+%28-2%2B-+sqrt%28+-12+%29%29%2F8+
x+=+%28-2%2B-+2%2Asqrt%28+-3+%29%29%2F8+
highlight%28x+=+%28-1%2B-+sqrt%28+3+%29i%29%2F4%29 where i=sqrt%28-1%29

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
formula is:

8x^3 - 1 = 0

add 3 to both sides of the equation to get:

8x^3 = 1

divide both sides of the equation by 8 to get:

x^3 = (1/8)

Take the cube root of both sides of the equation to get:

x = (1/8)^(1/3) which looks like x+=+%281%2F8%29%5E%281%2F3%29+

this can also be written as x = root(3,(1/8)) which looks like +root%283%2C%281%2F8%29%29+

you can use your calculator to solve this to get x = (1/2).

you can also see that +root%283%2C%281%2F8%29%29+ is the same as root%283%2C%281%2F2%29%2A%281%2F2%29%2A%281%2F2%29%29 which is the same as root%283%2C%281%2F2%29%5E3%29

You should also be able to see that root%283%2C%281%2F2%29%5E3%29 is the same as %28%281%2F2%29%5E3%29%5E%281%2F3%29 which is the same as %281%2F2%29%5E%283%2A%281%2F3%29%29 which becomes %281%2F2%29%5E1 which becomes %281%2F2%29.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Hi,
.
Solving for the "three" solutions of this cubic equation
+8x%5E3-1=0+
.
+x%5E3+-%281%2F8%29%5E3+=+0+
.
+%28x-+1%2F2%29%2A%28x%5E2+%2B+%281%2F2%29x+%2B+1%2F4+%29=+0+
.
%28x-+1%2F2%29=0 x = (1/2)
.
%28x%5E2+%2B+%281%2F2%29x+%2B+1%2F4%29=+0+
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solving using the quadratic equation results in 2 non-real numbers
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
.
x+=+%28-.5+%2B-+i%2Asqrt%28+.75+%29%29%2F%282%29+