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Math Help - quadratic

  1. #1
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    quadratic

    if the roots of the equation x^2-10cx-11d=0 are a,b and those of x^2-10ax-11b=0 are c,d then find the value of a+b+c+d(a,b,c,d real distinct numbers)?


    (ans=1210)
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  2. #2
    Senior Member pankaj's Avatar
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    Quote Originally Posted by abhishek arora View Post
    if the roots of the equation x^2-10cx-11d=0 are a,b and those of x^2-10ax-11b=0 are c,d then find the value of a+b+c+d(a,b,c,d real distinct numbers)?


    (ans=4)
    Boy,your answer is surely wrong

    a+b=10c

    c+d=10a

    a+b+c+d=10(a+c)

    b+d=9(a+c).Also we have a+b-c-d=10c-10a.Thus, b-d=11(c-a)

    Since a is root of x^2-10cx-11d=0,we have a^2-10ac-11d=0........(1)

    Since cis root of x^2-10ax-11b=0,we have c^2-10ac-11b=0.........(2)

    Subtracting (1) and (2)

    c^2-a^2=11(b-d)

    (a+c)(c-a)=121(c-a)

    (a+c)=121

    a+b+c+d=10(a+c)=1210
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