Question

Find the value of a and b such that
5+√3÷7+2√3=a-b√3​

Answer 1

$5 + \frac{ \sqrt{3} }{7} + 2 \sqrt{3} = a - b \sqrt{3}$

$5 + \frac{1 \sqrt{3} }{7} + 2 \sqrt{3} = a - b \sqrt{3}$

$5 + \frac{1 \sqrt{3} }{7} + \frac{2 \sqrt{3} \times 7}{1 \times 7} = a - b \sqrt{3}$

$5 + \frac{1 \sqrt{3} }{7} + \frac{14 \sqrt{3} }{7} = a - b \sqrt{3}$

$5 + \frac{15 \sqrt{3} }{7} = a - b \sqrt{3}$

Equating corresponding rational and irrational factors, we have

$a = 5$

$- b \sqrt{3} = \frac{15 \sqrt{3} }{7}$

√15 should be cncelled on both the sides

$- b = \frac{15}{7}$

$b = \frac{ - 15}{7}$

$so \: a = 5 \\ \\ b = \frac{ - 15}{7}$