Find the values of a and b if (7 + 3√5)/(3 + √5) – (7 − 3√5)/(3 − √5) = a+√5 b

Last updated at August 14, 2026 by

Find the values of a and b if (7 + 3√5)/(3 + √5) – (7 − 3√5)/(3 − √5)

Find the values of a and b if (7 + 3√5)/(3 + √5) – (7 − 3√5)/(3 − √5) = a+√5 b - Part 2
Find the values of a and b if (7 + 3√5)/(3 + √5) – (7 − 3√5)/(3 − √5) = a+√5 b - Part 3

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Transcript

Find the values of 𝑎 and 𝑏 if (7 + 3√5)/(3 + √5) – (7 − 3√5)/(3 − √5) = 𝑎+√5 𝑏 We have (7 + 3√5)/(3 + √5) – (7 − 3√5)/(3 − √5) = ((7 + 3√5))/((3 + √5)) × ((3 − √5))/((3 − √5)) – ((7 − 3√5))/((3 − √5)) × ((3 + √5))/((3 + √5)) = (7(3 − √5) + 3√5(3 − √5))/((3 + √5) (3 − √5)) = ((21 − 7 √5 + 9 √5 − 15))/((3 + √5) (3 − √5)) – ((21 + 7 √5 − 9 √5 − 15))/((3 − √5) (3 + √5)) = ((6 + 2√5))/((9 − 5))−((6 − 2√5))/((9 − 5)) = (6 + 2√5)/4−((6 − 2√5))/4 = (6 + 2√5 − 6 + 2√5)/4 = (4√5)/4 = √5 Comparing with a + √5 b Hence, a = 0 and b = 1

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