Question

5+2√3 /7+4√3= a+b√3 find the value of a and b.

Answer 1

Answer:

a = 11

b= -6

Step-by-step explanation:

5 + 2√3 ( 7- 4√3 ) / 7+4√3 ( 7-4 √3 )

35 - 20 √3 + 14√3 - 8 ×3 = 11 - 6√3

on comparing,

a = 11 , b = -6

Answer 2

Answer:

$\frac{5+2\sqrt{3} }{ 7+4\sqrt{3} } = \frac{5+2\sqrt{3} }{7+4\sqrt{3} }*\frac{7-4\sqrt{3} }{7-4\sqrt{3} } = \frac{35-20\sqrt{3}+14\sqrt{3}-24 }{(7)^{2}-(4\sqrt{3})^{2} } =\frac{11-6\sqrt{3}}{49-48} =11-6\sqrt{3}\\Therefore ,\\a=11 , b= -6\sqrt{3}$

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