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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1 Answer(s)

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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