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Math Help - 3 hard algebra problems!

  1. #1
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    3 hard algebra problems!

    Just can't figure out these 3 problems:


    Anyone help please?

    Thanks.
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  2. #2
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    Quote Originally Posted by xxravenxx View Post
    Just can't figure out these 3 problems:


    Anyone help please?

    Thanks.
    HI

    For the first problem ,

    x^2+ax-b=0 its roots are a and c

    a+c=-a ---1

    ac=-b ----2

    x^2+cx+d=0 its roots are b and d ,

    b+d=-c --- 3

    bd=d ---4

    From 4 , bd=d\Rightarrow b=1

    From 1 , 2a=-c

    At 2 , a(-2a)=-b

    2a^2=b

    2a^2=1

    a=\pm\frac{1}{\sqrt{2}}

    At 1 , 2(\pm\frac{1}{\sqrt{2}})=-c

    c=2(\mp\frac{1}{\sqrt{2}})

    c=\mp\sqrt{2}

    Then , from 2 ,

    1+d=-c

    1+d=\pm\sqrt{2}

     <br />
d=-1\pm\sqrt{2}<br />
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  3. #3
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    Quote Originally Posted by mathaddict View Post
    HI

    For the first problem ,

    x^2+ax-b=0 its roots are a and c

    a+c=-a ---1

    ac=-b ----2

    x^2+cx+d=0 its roots are b and d ,

    b+d=-c --- 3

    bd=d ---4

    From 4 , bd=d\Rightarrow b=1

    From 1 , 2a=-c

    At 2 , a(-2a)=-b

    2a^2=b

    2a^2=1

    a=\pm\frac{1}{\sqrt{2}}

    At 1 , 2(\pm\frac{1}{\sqrt{2}})=-c

    c=2(\mp\frac{1}{\sqrt{2}})

    c=\mp\sqrt{2}

    Then , from 2 ,

    1+d=-c

    1+d=\pm\sqrt{2}

     <br />
d=-1\pm\sqrt{2}<br />

    Thank you for giving the solution to Problem 4, however, could you please explain how you got that sign? I don't understand how you got from this:

    At 1 , 2(\pm\frac{1}{\sqrt{2}})=-c

    to this:

    c=2(\mp\frac{1}{\sqrt{2}})

    I have never come across that symbol before. Care to explain what it means please?


    And any one have solutions for the other two questions?
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  4. #4
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    Quote Originally Posted by xxravenxx View Post
    Thank you for giving the solution to Problem 4, however, could you please explain how you got that sign? I don't understand how you got from this:

    At 1 , 2(\pm\frac{1}{\sqrt{2}})=-c

    to this:

    c=2(\mp\frac{1}{\sqrt{2}})

    I have never come across that symbol before. Care to explain what it means please?


    And any one have solutions for the other two questions?
    \pm\frac{1}{sqrt{2}} means \frac{1}{sqrt{2}} or -\frac{1}{\sqrt{2}}

    Take for example  x^2=4

    x=\pm 2

    That means x can be 2 or -2 as well .

    Does that clear things up for you ?
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  5. #5
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    Quote Originally Posted by mathaddict View Post
    \pm\frac{1}{sqrt{2}} means \frac{1}{sqrt{2}} or -\frac{1}{\sqrt{2}}

    Take for example  x^2=4

    x=\pm 2

    That means x can be 2 or -2 as well .

    Does that clear things up for you ?
    Yea I know that symbol its just that upside down one that baffles me?
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  6. #6
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    Quote Originally Posted by xxravenxx View Post
    Yea I know that symbol its just that upside down one that baffles me?
    When you have , \pm 2

    -(\pm 2)=\mp 2

    2 \pm 3 = 5 or -1

    2\mp 3 = -1 or 5
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  7. #7
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    Quote Originally Posted by mathaddict View Post
    When you have , \pm 2

    -(\pm 2)=\mp 2

    2 \pm 3 = 5 or -1

    2\mp 3 = -1 or 5

    Alright. Thanks again.

    Any clue on the others? :S
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