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SSC Quantitative Aptitude Algebra Question Bank Elementary Algebra (I)

  • question_answer
    If \[a=\frac{2+\sqrt{3}}{2-\sqrt{3}}\]and \[b=\frac{2-\sqrt{3}}{2+\sqrt{3}},\]then the value of \[({{a}^{2}}+{{b}^{2}}+ab)\]is

    A) 195

    B) 200

    C) 175

    D) 185

    Correct Answer: A

    Solution :

    [a] Given \[a=\frac{2+\sqrt{3}}{2-\sqrt{3}}\]and \[b=\frac{2-\sqrt{3}}{2+\sqrt{3}}\] \[\therefore \]      \[{{a}^{2}}+{{b}^{2}}+ab={{(a+b)}^{2}}-ab\] \[=\left( \frac{2+\sqrt{3}}{2-\sqrt{2}}-\frac{2-\sqrt{3}}{2+\sqrt{3}} \right)\] \[={{\left[ \frac{2\,(4+3)}{4-3} \right]}^{2}}-1\] \[={{(14)}^{2}}-1=195\]


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