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If 5+2√3/ 7+4√3 = a + b√3, then find the values of a and b.

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If \(\frac {5+2\sqrt3}{7+4\sqrt3}\) = a + b√3, then find the values of a and b.

5+2√3/ 7+4√3

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Given that \(\frac {5+2\sqrt3}{7+4\sqrt3}\)

Now rationalise the denominator, 

(Rational Factor of 7+4√3 is 7- 4√3)

a + b√3 – 11 – 6√3 =11 + (-6)√3 

.’. a = 11, b = -6.

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