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## #1 2006-01-09 08:08:04

Rose-Red
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### weird equation

Could someone help me with this?

x³=6x+9

It doesn't seem difficult, but my answer doesn't suit to the answer in the book

## #2 2006-01-09 08:12:44

God
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### Re: weird equation

so basically x^3 - 6x - 9 = 0

We can factor out (x-3) from here, leaving
(x-3)(x^2+3*x+3) = 0

x-3 = 0, so x=3 is a solution

x^2 + 3x + 3 = 0
This can be solved easily using the quadratic formula

## #3 2006-01-09 08:20:59

Rose-Red
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### Re: weird equation

thanx man, but I did it in another more complicated way.

x³-9-6x=0
(x³-27)+18-6x=0
(x-3)(x²+27x+27²)-6(x-3)=0
(x-3)(x²+27x+723)=0

x-3=0
x=3

and
x²+27x+723=0
D<0 no solutions

Now the answer is correct.

Could u explain me how you get this (x^2+3*x+3)?

Last edited by Rose-Red (2006-01-09 08:21:57)

## #4 2006-01-09 08:25:16

irspow
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### Re: weird equation

God factored out x-3 from the original equation.  (x-3)(x²+3x+3) = x³-6x-9

## #5 2006-01-09 08:32:15

Rose-Red
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### Re: weird equation

but i dont understand how it is possible. I cant find any rule or formula that allows to do that

## #6 2006-01-09 08:34:08

God
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### Re: weird equation

By the rational roots theorem, the only possible rational solutions are -9 -3 -1 1 3 and 9
By the rule of signs, there is one sign change, so there is a positive root, so start with positive numbers.
After finding that 3 is a root, we know that we can factor out (x-3)

Use synthetic division to find out the remaining quadratic:

## #7 2006-01-09 08:38:31

Rose-Red
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### Re: weird equation

OMG I've never hear of that O_O
Thank you, I'll try to understand that and maybe use it later