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    Proof

    

\sqrt{a^{2} + b^{2}} \leq | a | + | b |
    Where or how do i start please

    Thanks
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    (Original post by Concav)
    Proof

    

\sqrt{a^{2} + b^{2}} \leq | a + b |
    Where or how do i start please

    Thanks
    a=1, b=-1

    \sqrt{a^{2} + b^{2}} \nleq | a + b |

    Disproved!
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    (Original post by ghostwalker)
    a=1, b=-1

    \sqrt{a^{2} + b^{2}} \nleq | a + b |

    Disproved!
    I think it's true if ab \ge 0.

    To the OP: consider the definition of the modulus: |x| = \sqrt{x^2}
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    (Original post by ghostwalker)
    a=1, b=-1

    \sqrt{a^{2} + b^{2}} \nleq | a + b |

    Disproved!
    (Original post by atsruser)
    I think it's true if ab \ge 0.

    To the OP: consider the definition of the modulus: |x| = \sqrt{x^2}
    Sorry edited
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    (Original post by Concav)
    Sorry edited
    Well you've got a square root there, so since both sides of your inequality are non-negative, I'd start by squaring them. A little bit of thinking from there may show you how the proof is done.
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    (Original post by ghostwalker)
    Well you've got a square root there, so since both sides of your inequality are non-negative, I'd start by squaring them. A little bit of thinking from there may show you how the proof is done.
    THAnks mate i love you can i ask you another
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    (Original post by Concav)
    THAnks mate i love you can i ask you another
    As long as you've thought about it for a while.
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    (Original post by ghostwalker)
    As long as you've thought about it for a while.
    I have its just ive been so inactive with maths for a while.
    How do i do
     | \dfrac{a}{b} + \dfrac{b}{a} | \geq 2
    Ive added both fractions but thats about it

    a, b not 0
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    (Original post by Concav)
    I have its just ive been so inactive with maths for a while.
    How do i do
     | \dfrac{a}{b} + \dfrac{b}{a} | \geq 2
    Ive added both fractions but thats about it

    a, b not 0
    Once you know how to do it, it's quite simple. But doesn't really help the learning process to just come out with it. So, again, I'll try and point in the general direction.

    So, you have the sum of two fractions. First thing I'd do is get a common denominator. Then use what you know about division and multiplication of modulii, to rearrange it into an equivalent form without the fractions.

    Then have a think about the resulting equation.

    PS: Post again if you need further assistance.
 
 
 
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