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



This Question is Closed

asnaseer
Best Response
You've already chosen the best response.
1
hint: Expand \((x+y)^2\)

samnatha
Best Response
You've already chosen the best response.
0
i'm sorry i'm still lost

asnaseer
Best Response
You've already chosen the best response.
1
what can you say about the number \((x+y)^2\)? can it ever be negative?

samnatha
Best Response
You've already chosen the best response.
0
yes

asnaseer
Best Response
You've already chosen the best response.
1
how?

asnaseer
Best Response
You've already chosen the best response.
1
remember x, y E R

samnatha
Best Response
You've already chosen the best response.
0
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

asnaseer
Best Response
You've already chosen the best response.
1
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 \(x^2+2xy+3y^2\)

samnatha
Best Response
You've already chosen the best response.
0
so the answere would be (x+y)^2 + y^2

asnaseer
Best Response
You've already chosen the best response.
1
not quite  what do you get when you expand \((x+y)^2\) ?

malevolence19
Best Response
You've already chosen the best response.
0
(x+y)^2+2y^2

samnatha
Best Response
You've already chosen the best response.
0
x^2 + 2xy + y ^2

asnaseer
Best Response
You've already chosen the best response.
1
correct  now what do you need to add to this in order to get to your original expression?

samnatha
Best Response
You've already chosen the best response.
0
2y to be squared

asnaseer
Best Response
You've already chosen the best response.
1
perfect!

asnaseer
Best Response
You've already chosen the best response.
1
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?

samnatha
Best Response
You've already chosen the best response.
0
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

asnaseer
Best Response
You've already chosen the best response.
1
yw :)
could you please post that as a separate question. thanks.

samnatha
Best Response
You've already chosen the best response.
0
using the same axsis and scales graph the functions f(x)=x
and g(x)= 2x  3

asnaseer
Best Response
You've already chosen the best response.
1
< I meant post in the list to the left

samnatha
Best Response
You've already chosen the best response.
0
oh ok sorry

asnaseer
Best Response
You've already chosen the best response.
1
np :)
it just helps posting each question separately as others can then see each question more easily and also learn from them. :)