How do I prove this?

analytically

>>8515757
What does that mean?

>>8515744
It's false

>>8515763
How do you know?

>>8515763
where are the proofs?

>>8515744
Move 4abcd to the other side of the inequality, take sqare root of both sides. This should immediately look like a familiar inequality, with minor complications.

>>8515805
Why don't you just do the proof? What you said makes little sense.

>>8515766
let them all equal 1 lol

>>8515744
It's false, consider

a = -2b, -c/12 < d < 0

divide by (b d)^2 set A=a/b, C = c/d, get
(A-C)^2 + 2 A + 2 C, and it's obvious

>>8515827
>a = -2b

They're all positive.

>>8515833
That's what you're supposed to prove.

>>8515821
[math](1*1+1*1+1*1)^2 - 4*1*1*1*1 > 0 \\ (3)^2 - 4 > 0 \\ 9-4>0 \\ 5>0[/math]

>>8515836
No, you're trying to prove the left expression given the right.

>>8515830
sorry, should be
(A-C)^2 + 2 A + 2 C + 1 > 0
where A = a/b, C=c/d. Still obvious.

The original expression is just
((a/b-c/d)^2 + 2 a/b + 2 c/d + 1)*(b d)^2 >0

>>8515812
I'm not doing your homework, you fucking mongoloid. Do exactly what I said. It's a simple application of AM-GM.

>>8515744
Move 4abcd to the right hand side, expand the term in parentheses, then do some algebra and you should be fine.

But your statement is meaningless. What numbers am I allowed use? It isn't true if I can use negatives.

>>8515841
you can replace a,b,c,d>0 with the weaker condition
a/b + c/d > 0

>>8515830
I think you've done it my friend. Thanks.

>>8515744
Get a really big computer and try all combinations of numbers smaller than 10^200, easy proof. This is how the goldbach conjecture was proven.

>>8515744
https://www.wolframalpha.com/input/?i=(a+d+%2B+b+c+%2B+b+d)%5E2+-+4+a+b+c+d+%3E+0

print this out and hand it to your teacher

(ad + bc)^2 - 4abcd > 0 is true when a,b,c,d > 0

>>8515744

(ad + bc + bd)^2 - 4abcd > 0

root ((ad + bc + bd)^2) >root( 4abcd)

(ad + bc + bd)^2 >2root(abcd)

Onli if a,b,c,d>0

>>8515990

ad + bc + bd >2root(abcd)

Only if a,b,c,d>0

>>8515821
You retard lmao