Question

Find the value of a and b if 5-2√3÷7-4√3=a-√3b

Answer 1

Answer:

a = 11 and b = -6

Step-by-step explanation:

$\frac{5 - 2 \sqrt{3} }{7 - 4 \sqrt{3} }$

Rationalizing the denominator we get:

$= \frac{5 - 2 \sqrt{3} }{7 - 4 \sqrt{3} } \times \frac{7 + 4 \sqrt{3} }{7 + 4 \sqrt{3} } \\ \\ = \frac{5(7 + 4 \sqrt{3}) - 2 \sqrt{3}(7 + 4 \sqrt{3} ) }{ {(7)}^{2} - {(4 \sqrt{3} )}^{2} } \\ \\ = \frac{35 + 20 \sqrt{3} - 14 \sqrt{3} - 24}{49 - 48} \\ \\ \bf = 11 + 6 \sqrt{3} \:$

Now, equating L.H.S and R.H.S we get:

$11 + 6 \sqrt{3} = a - b \sqrt{3} \\ \\ \bf a = 11 \: \:and \: \: b = - 6$