Question

pls find the rational numbers a and b here. Best answer will definitely be marked the brainliest.

Answer 1

here is the correct answer with explanation for ur question

Answer 2

Hey friend,
Here is the answer you were looking for:
$\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } = a + b \sqrt{3} \\ \\ on \: rationalizing \: the \: denominator\: we \: get \\ \\ = \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} } \\ \\ using \: the \: identity \\ (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ = \frac{5 \times 7 - 5 \times 4 \sqrt{3} + 2 \sqrt{3} \times 7 - 2 \sqrt{3} \times 4 \sqrt{3} }{ {(7)}^{2} - {(4 \sqrt{3}) }^{2} } \\ \\ = \frac{35 - 20 \sqrt{3} + 14 \sqrt{3} - 24 }{49 - 48} \\ \\ 11 - 6 \sqrt{3} = a + b \sqrt{3} \\ \\ a = 11 \\ \\ b = - 6$


Hope this helps!!!!

@Mahak24

Thanks...
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