# Solving Cubic Equations

• May 18th 2009, 12:26 AM
22upon7
Solving Cubic Equations
Hi,

Could you please explain how to solve these two sums, step by step please.

1. $2x^3=16x$
2. $2(x-1)^3=32$

This is as far as I got on both sums:

1.
$2x^3=16x$
$x^3=8x$
$x^2=8$
$x^2-8=0$

2.
$2(x-1)^3=32$
$(x-1)^3=16$
$(x-1)^3-16=0$

Any help would be greatly appreciated,

Thanks,

Dru
• May 18th 2009, 12:32 AM
Rapha
Hi.

Quote:

Originally Posted by 22upon7
Hi,

Could you please explain how to solve these two sums, step by step please.

1. $2x^3=16x$
2. $2(x-1)^3=32$

This is as far as I got on both sums:

1.
$2x^3=16x$
$x^3=8x$
$x^2=8$
$x^2-8=0$

Good thinking, but you made a mistake

$x^3=8x$

OKAY

$x^2=8$

Not okay, you divided by x; you can do that, but this is only for $x \not= 0$; and x = 0 is a solution!

So

$x^3=8x$

$x^3-8x = 0$

$x(x^2-8) = 0$

is better,

now you know x = 0 is a solution and x²-8 = 0 leads to the other solutions; you still have to solve x²-8= 0, tho.

Quote:

Originally Posted by 22upon7
2.
$2(x-1)^3=32$
$(x-1)^3=16$
$(x-1)^3-16=0$

The last step seems to be unnecessary

$(x-1)^3=16$ // ^(1/3)

$x-1 = 16^{1/3}$

$x = 16^{1/3}+1$

Quote:

Originally Posted by 22upon7
Any help would be greatly appreciated,

Thanks,

You're welcome.

Yours, Rapha