/sci/ - Easy math problem

Name: Anonymous 2009-09-12 22:38

Well, it doesn't look hard and I feel extremely retarded for not being able to figure it out but....HOW THE FUCK DO YOU SOLVE....

a^3 + (1/2)a = 9 ?!?!?!?!

Name: Anonymous 2009-09-12 23:04

Solution of a cubic with no squared term:

If f = x^3 + px + q, then

x = \sqrt[3]{-\frac{q}{2}+\sqrt{\frac{q^{2}}{4}+\frac{p^{3}}{27}}}+\sqrt[3]{-\frac{q}{2}-\sqrt{\frac{q^{2}}{4}+\frac{p^{3}}{27}}}

Just plug in p=1/2 and q=-9.

http://en.wikipedia.org/wiki/Cubic_function#Cardano.27s_method

Name: Anonymous 2009-09-12 23:05

>>2
Did tex stop working for everyone, or just me? :/

Name: Anonymous 2009-09-13 14:52

a^3+(1/2)a=9
a^3+(a/2)=9
2a^3+a=18
2a^3+a-18=0
(a-2)(2a^2+4a+9)=0
a-2=0
a=2

Name: Anonymous 2009-09-13 15:18

easy; people always over-complicate this stuff:

a^3 + (1/2)a = 9
-a/2 -a/2
a^3 = 9-a/2 =
a^3 = (4.5-a)/2
*2 *2
2a^3 = 4.5 - a
-4.5 -4.5
2a^3 - 4.5 = -a
*-1 *-1
4.5 - 2a^3 = a
so a = 4.5 - 2a^3 which means a is probobly a little more than zero?

Name: Anonymous 2009-09-13 17:32

>>4
I know its in there, but how in fuck all did you pull that (a-2) out of that frrgarble?
>>5
Your post contains irony, please fix.

Name: Anonymous 2009-09-13 19:51

ironic math is the best!

Name: Anonymous 2009-09-13 21:52

>>6
You can long-divide 2a³+a-18 by a-2 to see that 2a³+a-18 = (a-2)(2a²+4a+9)

http://en.wikipedia.org/wiki/Polynomial_long_division
should tell you how its done, although the (a-2) is a bit of a guess at this point, you can use:
http://en.wikipedia.org/wiki/Synthetic_division
Scroll down to "Polynomial root-finding" to find the possible roots; in this case, 2 is a possible root so you check by dividing by a-2.

Name: Anonymous 2009-09-13 22:43

Liek dis: http://i28.tinypic.com/24w832q.jpg

Name: Anonymous 2009-09-16 7:20

Depress it.

Name: Anonymous 2009-09-19 21:39

Hrm, anyone wanna either correct or agree with -
a^3 + (1/2)a = 9
a^3 + a/2 = 9
a^3 + a = 18
(cuberoot)a^3 + a = (cuberoot)18
a + a = 2.62074139
a = 1.310

Name: Anonymous 2009-09-19 21:40

Hrm, anyone wanna either correct or agree with -
a^3 + (1/2)a = 9
a^3 + a/2 = 9
a^3 + a = 18
(cuberoot)a^3 + a = (cuberoot)18
a + a = 2.62074139
a = 1.310

Name: Anonymous 2009-09-20 0:51

>>13
>a^3 + a/2 = 9
>a^3 + a = 18
in this part it should be
>a^3 + a/2 = 9
>(*2)
>2a³+a=18
as >>4 made

Easy math problem

1 Name: Anonymous 2009-09-12 22:38

2 Name: Anonymous 2009-09-12 23:04

3 Name: Anonymous 2009-09-12 23:05

4 Name: Anonymous 2009-09-13 14:52

5 Name: Anonymous 2009-09-13 15:18

6 Name: Anonymous 2009-09-13 17:32

7 Name: Anonymous 2009-09-13 19:51

9 Name: Anonymous 2009-09-13 21:52

10 Name: Anonymous 2009-09-13 22:43

11 Name: Anonymous 2009-09-16 7:20

13 Name: Anonymous 2009-09-19 21:39

14 Name: Anonymous 2009-09-19 21:40

15 Name: Anonymous 2009-09-20 0:51