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If 1/7 - 4√3 = a + b√3, then find the value of a^3 + b^3.

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If 1/7 - 4√3 = a + b√3, then find the value of a3 + b3.

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The Rationalising Factor of 7 – 4√3 and √3 – 2 is 7 + 4√3 and √3 + 2

= 7 + 4√3 – √3 – 2 

= 5 + 3√3 = a + b√3 

Here a = 5,b = 3

∴ a3 + b3 = (5)3 + (3)3 = 125 + 27 = 152

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