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Thread: Inequalities help!!!

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    Inequalities help!!!

    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!!!

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    Re: Inequalities help!!!

    Quote Originally Posted by billjyang View Post
    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.
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    Re: Inequalities help!!!

    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
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    Cadet JustRandomThings's Avatar
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    Re: Inequalities help!!!

    Quote Originally Posted by fluffchuck View Post
    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
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