Find the values of a and b in (3 - √5) / (3 + 2√5) = (a√5 - b) / 11
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3 - √5 = (3 - √5) * (3 - 2√5)
3 + 2√5 (3 + 2√5) (3 - 2√5)
= (9 - 6√5 - 3√5 +10) / [9 - (4 * 5)]
= 19 - 9√5 / -11
= - 19 + 9√5 / 11 (bringing - sign to the numerator)
= - 19 + 9√5 / 11 = (a√5 - b) / 11
= - 19 + 9√5 = a√5 - b
a = 9
b = 19
3 + 2√5 (3 + 2√5) (3 - 2√5)
= (9 - 6√5 - 3√5 +10) / [9 - (4 * 5)]
= 19 - 9√5 / -11
= - 19 + 9√5 / 11 (bringing - sign to the numerator)
= - 19 + 9√5 / 11 = (a√5 - b) / 11
= - 19 + 9√5 = a√5 - b
a = 9
b = 19
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