Does anybody have any insight on how to solve this?

I have never seen a problem like this. It looks like there may be a clever solution though.

>>8518246
x^3+3x^2-7x+1
=(x-a)(x-b)(x-c)
=x^3-(a+b+c)x^2+(ab+ac+bc)x-abc

a^2+b^2+c^2
=(a+b+c)^2-2(ab+ac+bc)
=(-3)^2-2(-7)
=9+14
=23

File: roots.png (15KB, 526x353px) Image search: [Google]

15KB, 526x353px

>>8518246
here are your roots
answer is simply the first root squared + the second root squared + the third root squared

>>8518269
I know how to wolfram. I don't think Cardano's cubic formula is the answer, there must be a clever solution.

File: VUCQhHl.png.jpg (13KB, 480x270px) Image search: [Google]

13KB, 480x270px

>>8518270
see
>>8518267

File: roots_approx.png (21KB, 520x463px) Image search: [Google]

21KB, 520x463px

>>8518270
>I know how to wolfram
then what's the problem?
all you gotta do is plug it in and you're done
pic related is the approximate

no thought required

Think I have a decent start:
x^3 + 3x^2 -7x +1 = (x-a)(x-b)(x-c) = x^3 - (a+b+c)x^2 + (ab + bc + ca)x - abc.

Thus 3 = a+b+c, -7 = ab + bc + ca, abc = -1

File: 1475231192293.png (25KB, 199x200px) Image search: [Google]

25KB, 199x200px

>>8518277
can people not see this post or something?
>>8518267

>>8518276
this problem is meant to be done in test format without access to internet

>>8518280
are calculators banned? because this is literally a calculator problem
in the real world, you plug it into a calculator and you get the right answer in a matter of seconds

>>8518279
I was still working it out while he was posting, brainlet that I am. Neat problem though.

>>8518267
Wow, that was actually clever. +1 for u

>>8518267
>>8518277
Thank you that was exactly what I was hoping for.

https://en.wikipedia.org/wiki/Symmetric_polynomial

File: this-motherfucker-knows.png (155KB, 459x306px) Image search: [Google]

155KB, 459x306px

>>8518267

>>8518267
Wish I could give this more than one (you)

File: MisterTao.jpg (297KB, 2048x1365px) Image search: [Google]

297KB, 2048x1365px

>>8518267
Mister Tao, sir, why are you wasting your time on 4chan's /sci/?

File: f.jpg (50KB, 435x571px) Image search: [Google]

50KB, 435x571px

>>8518267
Just when I thought I was smart this motherfucker shows up.

>>8518246
a=0
b=0
c=0

Leading us to

a2=0
b2=0
c2=0

OR

02+02+02

>>8518246
>a, b, c be zeros of

What did he mean by this?

>>8518267
This is pretty trivial. What's so genius about it?

>>8519521
It is. /sci/ is full of dumbfucks.

>>8519521
Of course it's trivial once you see the results, and given enough time I think most people here would have found the solution.

But most people here are just here for memes