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JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Solution of quadratic equations and Nature of roots

  • question_answer
    If \[{{\log }_{2}}x+{{\log }_{x}}2=\frac{10}{3}={{\log }_{2}}y+{{\log }_{y}}2\] and \[x\ne y,\] then \[x+y=\] [EAMCET 1994]

    A) 2

    B) 65/8

    C) 37/6

    D) None of these

    Correct Answer: D

    Solution :

    We have \[{{\log }_{2}}x+\frac{1}{{{\log }_{2}}x}=3+\frac{1}{3}={{\log }_{2}}y+\frac{1}{{{\log }_{2}}y}\] \ \[{{\log }_{2}}x=3,{{\log }_{2}}y=\frac{1}{3}\] \[(\because x\ne y)\] Þ \[x={{2}^{3}}\]and\[y={{2}^{1/3}}\Rightarrow x+y=8+{{2}^{1/3}}\].


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