Question

If a,b are rational number and 2+3√3/4-5√3= a+b√5, find the values of a and b.

Answer 1

Answer:

the values a = 7 and b = 4

Explanation:

$if \: \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } = a \: + b \sqrt{3} \\ = \frac{( {2 + \sqrt{3} })^{2} }{(2 - \sqrt{3}) +(2 + \sqrt{3} ) } = a + b \sqrt{3} \\ = \frac{4 + 3 + 4 \sqrt{3} }{ {(2}^{2}) - ( { \sqrt{3} }^{2}) } = a + b \sqrt{3} \\ = \frac{7 + 4 \sqrt{3} }{4 - 3} = a \: + b \: \sqrt{3} \\ = 7 + 4 \sqrt{3} = a + b \sqrt{3} \\ compare \: both \: the \: sides \:$

so we get the value A = 7 and B = 4