Question

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

Answer 1

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

Answer 2

i'm sorry i'm still lost

Answer 3

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

Answer 4

yes

Answer 5

how?

Answer 6

remember x, y E R

Answer 7

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

Answer 8

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 \(x^2+2xy+3y^2\)

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

x^2 + 2xy + y ^2

Answer 13

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

Answer 14

2y to be squared

Answer 15

perfect!

Answer 16

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?

Answer 17

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|

Answer 18

yw :)

could you please post that as a separate question. thanks.

Answer 19

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

Answer 20

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

Answer 21

oh ok sorry

Answer 22

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