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9th Class Mathematics Number System and its Operations Question Bank Number Systems

  • question_answer
    If \[\frac{(\sqrt{3}-1)}{(\sqrt{3}+1)}=(a-b\sqrt{3}),\] find the values of a and b.

    A) \[a=1,b=2\]                  

    B)  a = 2,b = 1                 

    C)  a = 2, b = 3   

    D)  a = 3, b = 2

    Correct Answer: B

    Solution :

    We have, \[a-b\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}\] \[=\frac{(\sqrt{3}-1)}{(\sqrt{3}+1)}\times \frac{(\sqrt{3}-1)}{\sqrt{3}+1}=\frac{{{(\sqrt{3}-1)}^{2}}}{3-1}\] \[=\frac{3+1-2\sqrt{3}}{2}=\frac{4-2\sqrt{3}}{2}=2-\sqrt{3}\] On comparing, we get \[a=2,b=1\]


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