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# x^4-3x^3+2=0

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CEO
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x^4-3x^3+2=0 [#permalink]  07 Jan 2009, 14:23
$$x^4-3x^3+2=0$$

Only real solutions

SVP
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Re: Solve the equation [#permalink]  07 Jan 2009, 22:35
GMATBLACKBELT wrote:
Only real solutions

x^4-3x^3+2=0.

x^4 - 3x^3 + 2 = 0
x^4 - 1 - 3x^3 + 3 = 0
[(x^2 + 1) (x^2 - 1)] -[3(x^3 - 1)] = 0
[(x^2 + 1) (x + 1) (x-1)] - [3 (x-1) (x^2 + x + 1)] = 0
(x-1) [(x^2 + 1) (x+1) - 3 (x^2 + x + 1) = 0
(x-1) (x^3 + x^2 + x + 1 - 3x^2 - 3x - 3) =0
(x-1) (x^3 - 2x^2 - 2x - 2) = 0

(x-1) = 0 --->
x = 1

x^3 - 2x^2 - 2x - 2 = 0
?????????????

Thats it.............
_________________
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Re: Solve the equation [#permalink]  08 Jan 2009, 11:57
Are these some sort of GMAT questions for us to solve the equations?
Intern
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Re: Solve the equation [#permalink]  08 Jan 2009, 23:56
x^4-3x^3+2 = 0

0=(x^3-1)(x-2)-(x^3-x)
0=(x-1)(x^2+x+1)(x-2)-x(x^2-1)
0=(x-1)(x^2+x+1)(x-2)-x(x-1)(x+1)
0=(x-1)[(x^2+x+1)(x-2)-x(x+1)]
x=1

then [(x^2+x+1)(x-2) - x(x+1)] =0
=x^3+x^2+x-2x^2-2x-2-x^2-x
=x^3-2x^2-2x-2 = 0

ohhhhhh headache i'll try to do it later
Re: Solve the equation   [#permalink] 08 Jan 2009, 23:56
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