JEE Main & Advanced Mathematics Sequence & Series Question Bank Self Evaluation Test - Sequences and Series

  • question_answer
    x and y are positive number. Let g and a be G. M. and AM of these numbers. Also let G be G.M. of x + 1 and y + 1. If G and g are roots of equation\[{{x}^{2}}-5x+6=0\], then

    A) \[x=2,\,y=\frac{3}{4}\]

    B) \[x=\frac{3}{4},y=12\]

    C) \[x=\frac{5}{2},y=\frac{8}{5}\]

    D) \[x=y=2\]

    Correct Answer: D

    Solution :

    [d] The roots of equation are 2 and 3 \[\therefore \,\,\,g=\sqrt{xy}=2\Rightarrow xy=4\] \[G=\sqrt{(x+1)(y+1)}=3\Rightarrow (x+1)(y+1)=9\] \[\therefore \,\,\,x=y=2\]


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