Inequalities help!!! (1 Viewer)

[billjyang]

I was wondering how I could do this question:
If (ad+bc)² <= (a²+b²)(c²+d²),
deduce that:
(a+b)²<= 2(a²+b²)

Now, I know that I am able to do it without the first property given, but the original question is a HENCE question... so i was wondering how to do it using the property above.
I can let c and d = 1, but I am not sure whether you can replace them with integer values.
A worked out solution will help me lots in easing up confusion with inequalities.
THANKS GUYS!!!

 

[pikachu975]

I was wondering how I could do this question:
If (ad+bc)² <= (a²+b²)(c²+d²),
deduce that:
(a+b)²<= 2(a²+b²)

Now, I know that I am able to do it without the first property given, but the original question is a HENCE question... so i was wondering how to do it using the property above.
I can let c and d = 1, but I am not sure whether you can replace them with integer values.
A worked out solution will help me lots in easing up confusion with inequalities.
THANKS GUYS!!!

Pretty sure you're allowed to since (ad+bc)^2 <= (a^2+b^2)(c^2+d^2) is an identity and hence should work with all a,b,c,d (except restrictions which don't seem to be given) so c =1 and d = 1 should work.

 

[fluffchuck]

The given identity has no restrictions on a,b,c,d except that they all must be real. Letting c=1 and d=1 should be correct

 

[JustRandomThings]

The given identity has no restrictions on a,b,c,d except that they all must be real. Letting c=1 and d=1 should be correct

Bill that question's not gonna appear on our test lmao. Webber told us remember? Only basic identities lmao