Simplify:
If 3+√7 / 3-√7 = a+b√7 find a and b
Answer: (8, 3)
Solution:-
(3 + √7)/(3 – √7) = a + b√7
(3 + √7) (3 + √7) /(3 – √7) (3 + √7) = a + b√7
{3² + (√7)² + 2 x 3 x √7}/{3² – (√7)²} = a + b√7
(9 + 7 + 6√7)/(9 – 7) = a + b√7
(16 + 6√7)/2 = a + b√7
8 + 3√7 = a + b√7
Comparing on both side,
Then, the value of a = 8 & b = 3
Hence, the correct answer is (8, 3).
