Question

if x+y=1 and x^2+y^2=4, what is x^3+y^3

Answer 1

weird precalc question i got today no idea how to do it

Answer 2

@Nnesha @iambatman

Answer 3

@StudyGurl14

Answer 4

\[(x+y)^3 = x^3+3x^2y+3xy^2+y^3\]
\[(x+y)^2 = x^2+2xy+y^2\]

This should be all you need :)

Answer 5

im gonna give it try.

Answer 6

Sounds good, I'll give you some more hints if you need them later. :D

Answer 7

the formula is just the most simplfied versions of

x^3+y^3=(x+y)(x^2-xy+y^2) right?

Answer 8

you have the formula. All you have to do is just input the given Info

Answer 9

im just confused on whether im suppose to use the x^3+Y^2 formula or (x+y)^3

Answer 10

(x+y)(x^2-xy+y^2)=(1)(4-xy)

Answer 11

\[(x+y)^3 = x^3+3x^2y+3xy^2+y^3\]
\[(x+y)^3 = x^3+y^3 + 3xy(x+y)\]
\[(x+y)^3 - 3xy(x+y)= x^3+y^3\]
So I arranged it so we have \(x^3+y^3\) which is what we want, and we know that \(x+y=1\) so we plug it in now:
\[1^3 - 3xy(1)=1-3xy = x^3+y^3\]
What's xy? Let's use this:
\[(x+y)^2 = x^2+2xy+y^2\]
\[\frac{(x+y)^2 - (x^2+y^2)}{2} = xy\]
\[\frac{1^2 - 4}{2} =\frac{-3}{2} = xy\]
Now we can plug it in:

\[1-3 \frac{-3}{2} = x^3+y^3\]

Answer 12

im seeing what you did but if I had started with the formula (x+y)(x^2-xy+y^2)

if i plug in from there I get 4-xy? could i continue form here?

Answer 13

Yeah It looks like that'd probably work too

Answer 14

im not sure what to do from there though

Answer 15

do i use the same formula ?

Answer 16

Use(x+y)^2=x^2+2xy+y^2 from there

Answer 17

And solve for xy

Answer 18

Oh I think I got it.


1^2=4+2xy

1-4=-3

-3/2=2xy

xy=-3/2

1(4-3/2)=x^3+y^3

Answer 19

can you check for me? and how would you know which formula to use? it seems like you would need more than 1 to compute all the variables

Answer 20

you will end up with ×y =-3/2 so (1) (4-xy)=4-(-3/2)= 4+3/2= x^3 + y^3

Answer 21

oh, dumb negative mistake by me. this is kind of confusing because i never substituted formulas to solve questions like this. normally, how would you know which formulas to use?

Answer 22

like how we used x^3+y^3 then to (x+y)^2?

Answer 23

Try to reason through it using the Known formulas

Answer 24

you are right. this is only my first question with this, i just need to practice more. thank you both so much.