- A3/2
- B−1/2
- C1/2
- D2
Step-by-Step Solution
Multiply above and below by 3 − √5. Numerator: (7 + 3√5)(3 − √5) = 21 − 7√5 + 9√5 − 15 = 6 + 2√5. Denominator: 9 − 5 = 4. So the value is (6 + 2√5)/4 = 3/2 + (1/2)√5, giving b = 1/2.
Answer: C) 1/2
If (7 + 3√5)/(3 + √5) = a + b√5 where a and b are rational, then b equals:
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