Question

If both a and b are rational numbers , find the values of a and b 5+√3 upon 7−4√3 = a + √3 b​ pls

Answer 1

Step-by-step explanation:

$\frac{5 + \sqrt{3} }{7 - 4 \sqrt{3} } \\ = \frac{5 + \sqrt{3} }{7 - 4 \sqrt{3} } \times \frac{7 + 4 \sqrt{3} }{7 + 4 \sqrt{3} } \\ = \frac{35 + 20 \sqrt{3} + 7 \sqrt{3} + 12}{49 - 48 } \\ = \frac{47 + 27 \sqrt{3} }{1} \\ = 47 + 27 \sqrt{3}$

$\frac{5 + \sqrt{3} }{7 - 4 \sqrt{3} } = a + b \sqrt{3} \\ = > 47 + 27 \sqrt{3} = a + b \sqrt{3} \\ = > a = 47 \\ = > b = 27$