4 + 3 root5/4 - 3 root5 =a+b root5
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= 4 + 3√5 / 4 - 3√5
= 4 + 3√5 / 4 - 3√5 × 4 + 3√5 / 4 + 3√5
= [ (4)² + 2 (4) (3√5) + (3√5)² ] / (4)² - (3√5)²
= ( 16 + 45 + 24√5 ) / 16 - 45
= ( 61 + 24√5 ) / - 29
= - 61 / 29 -24 / 29 × √5
∴a = - 61/29 and b = - 24 / 29
= 4 + 3√5 / 4 - 3√5 × 4 + 3√5 / 4 + 3√5
= [ (4)² + 2 (4) (3√5) + (3√5)² ] / (4)² - (3√5)²
= ( 16 + 45 + 24√5 ) / 16 - 45
= ( 61 + 24√5 ) / - 29
= - 61 / 29 -24 / 29 × √5
∴a = - 61/29 and b = - 24 / 29
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Answer:
a= 61/ -29
b= 24/ -29
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