Question

find the value for a and b in the following if 1) 4√3/2-√3 = a + b √3​

Answer 1

$\large\red{\mathfrak{Hii\: mate\:, \: here's\: ur\: answer}}$

• For fiding the value of a and b, denominator must be rationalised.

$\large\pink{\sf{Rationalising :-}}$

$\frac{4 - \sqrt{2} }{2 - \sqrt{3} } = \frac{4 - \sqrt{2} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } = \frac{(4 - \sqrt{2})(2 + \sqrt{3})}{(2 - \sqrt{3})(2 + \sqrt{3)} } \\ \\ = \frac{8+4 \sqrt{3}-2 \sqrt{2} - \sqrt{6} }{4 - 3} = 8+4 \sqrt{3}-2 \sqrt{2} - \sqrt{6}$

$\green{ \bf{on \: comparing \: with \: \: a + b \sqrt{3} }} \\ \blue{ \sf{a = 8 \: and \: b \: = 4}}$

HOPE IT HELPS YOU ✨