Question

if 4+3√5/4-3√5=a+b√5then find a and b

Answer 1

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4 + 3√5 / 4 - 3√5 = a + b√5

=> (4 + 3√5) × (4 + 3√5) / (4 - 3√5) × (4 + 3√5) = a + b√5

=> (4 + 3√5)^2 / (4)^2 - (3√5)^2 = a + b√5

=> (4)^2 + (3√5)^2 + 2 × 4 × 3√5 / 16 - 45 = a + b√5

=> 16 + 45 + 24√5 / - 29 = a + b√5

=> 61 + 24√5 / -29 = a + b√5

=> - 61 - 24√5/29 = a + b√5

Hence ,

a = -61/29

b√5 = -24√5/29

b = -24/29






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