If 3+√7 / 3-√7 = a+b√7 find a and b

If 3+√7 / 3-√7 = a+b√7 find a and b

San Default Asked on 19th May 2016 in Maths.
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    Answer: 8, 3

    Solution:-
    (3 + sqrt.7)/(3 – sqrt.7)  = a + b sqrt.7
    (3 + sqrt.7) (3 + sqrt.7)/(3 – sqrt.7) (3 + sqrt.7) = a + b  sqrt.7
    (3 + sqrt.7)^2/3^2 – (sqrt.7)^2 = a + b sqrt.7
    {(3)^2 + (sqrt.7)^2 + 2 x 3 x sqrt.7}/(9 – 7)  = a + b sqrt.7
    {9 + 7 + 6 sqrt.7}/2 = a + b sqrt.7
    (16 + 6 sqrt.7)/2 = a + b sqrt.7
    8  + 3 sqrt.7 = a + b sqrt.7
    Comparing on both side,
    a =  8  and  b = 3

    Then, the value of a and b are 8 and 3.

    Hence, the correct answer is 8, 3.

    Anurag Mishra Professor Answered on 19th May 2016.
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