## dtan5457 one year ago if x+y=1 and x^2+y^2=4, what is x^3+y^3

1. dtan5457

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

2. dtan5457

@Nnesha @iambatman

3. dtan5457

@StudyGurl14

4. Empty

$(x+y)^3 = x^3+3x^2y+3xy^2+y^3$ $(x+y)^2 = x^2+2xy+y^2$ This should be all you need :)

5. dtan5457

im gonna give it try.

6. Empty

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

7. dtan5457

the formula is just the most simplfied versions of x^3+y^3=(x+y)(x^2-xy+y^2) right?

8. Hero

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

9. dtan5457

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

10. Hero

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

11. Empty

$(x+y)^3 = x^3+3x^2y+3xy^2+y^3$ $(x+y)^3 = x^3+y^3 + 3xy(x+y)$ $(x+y)^3 - 3xy(x+y)= x^3+y^3$ 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: $1-3 \frac{-3}{2} = x^3+y^3$

12. dtan5457

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?

13. Empty

Yeah It looks like that'd probably work too

14. dtan5457

im not sure what to do from there though

15. dtan5457

do i use the same formula ?

16. Hero

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

17. Hero

And solve for xy

18. dtan5457

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

19. dtan5457

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

20. Hero

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

21. dtan5457

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?

22. dtan5457

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

23. Hero

Try to reason through it using the Known formulas

24. dtan5457

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