Question

if r and s are solutions of x^2 + 6x - 2 = 0, what is the value of r^3 + s^3.

Answer 1

guess there is no choice to to actually solve

Answer 2

Yeah try using the quadratic formula to find r and s

Answer 3

funny how the same questions keep popping up

Answer 4

If r and s are the solutions, then r+s=-6 and rs=-2.
\[r^3+s^3=(r+s)(r^2-rs+s^2)=(r+s)((r+s)^2-3rs)=(-6)(36+6)=-252\]

Answer 5

cool, a snap way! but i can't see it all

Answer 6

What does the addition of the two zeroth solutions represent?

Answer 7

Is there something special about it?

Answer 8

In a quadratic equation ax^2+bx+c=0, the solutions add up to -b/a while their product is c/a.

Answer 9

sum of roots is \(-\frac{b}{a}\), product of roots is \(\frac{c}{a}\) and that cool trick was to write the sum of the cubes in terms of those. i will have to try to remember this

Answer 10

I never learned this. Wow

Answer 11

Cool trick

Answer 12

i never would have thought of
\[r^3+s^3=(r+s)(r^2-rs+s^2)=(r+s)((r+s)^2-3rs)\]

Answer 13

Ah, the wonders of algebra. =))

Answer 14

thx you were a big help

Answer 15

No problem. :D