# If 3+√7 / 3-√7 = a+b√7 find a and b

If 3+√7 / 3-√7 = a+b√7 find a and b

**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.