## samnatha 3 years ago prove that x²+2xy+3y²≥0 for all x, y E R

1. asnaseer

hint: Expand \((x+y)^2\)

2. samnatha

i'm sorry i'm still lost

3. asnaseer

what can you say about the number \((x+y)^2\)? can it ever be negative?

4. samnatha

yes

5. asnaseer

how?

6. asnaseer

remember x, y E R

7. samnatha

well i thought anything squared would be true bit i can't get the two brackets the same as i can't get 3y squared

8. asnaseer

try and first expand \((x+y)^2\) and then see what else you need to add to this in order to get your original expression of \(x^2+2xy+3y^2\)

9. samnatha

so the answere would be (x+y)^2 + y^2

10. asnaseer

not quite - what do you get when you expand \((x+y)^2\) ?

11. malevolence19

(x+y)^2+2y^2

12. samnatha

x^2 + 2xy + y ^2

13. asnaseer

correct - now what do you need to add to this in order to get to your original expression?

14. samnatha

2y to be squared

15. asnaseer

perfect!

16. asnaseer

so we end up with:\[x^2+2xy+3y^2=(x+y)^2+2y^2\]now - can you see that this can never be negative?

17. samnatha

ok thanks while i have you i have to do this using the same axsis and scales graph the functions f(x)=|x| and g(x)= |2x - 3|

18. asnaseer

yw :) could you please post that as a separate question. thanks.

19. samnatha

using the same axsis and scales graph the functions f(x)=|x| and g(x)= |2x - 3|

20. asnaseer

<--- I meant post in the list to the left

21. samnatha

oh ok sorry

22. asnaseer

np :) it just helps posting each question separately as others can then see each question more easily and also learn from them. :)