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

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asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.1hint: Expand \((x+y)^2\)

samnatha
 3 years ago
Best ResponseYou've already chosen the best response.0i'm sorry i'm still lost

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

samnatha
 3 years ago
Best ResponseYou've already chosen the best response.0well 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
 3 years ago
Best ResponseYou've already chosen the best response.1try 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
 3 years ago
Best ResponseYou've already chosen the best response.0so the answere would be (x+y)^2 + y^2

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

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

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.1so 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
 3 years ago
Best ResponseYou've already chosen the best response.0ok 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
 3 years ago
Best ResponseYou've already chosen the best response.1yw :) could you please post that as a separate question. thanks.

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

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.1< I meant post in the list to the left

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