Question

Find the values of a and b.
The answer is a= 11 b= -6.
Please Explain.

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Answer 1

Answer:

$\frac{5+2\sqrt{3} }{7+4\sqrt{3} }=a+b\sqrt{3}\\\frac{(5+2\sqrt{3})(7-4\sqrt{3})}{(7+4\sqrt{3})(7-4\sqrt{3})}\\=\frac{35-20\sqrt{3}+14\sqrt{3}-24}{49-48}=35-6\sqrt{3}-24\\=11-6\sqrt{3} \\a+b\sqrt{3}=11-6\sqrt{3}\\a = 11, b=-6$

Answer 2

Answer:

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