Question

if a and b are rational number find the value a and b in each of the following equations √3+√2/√3-√2=a+b√30​

Answer 1

Answer:

$a = 5 \: and \: b = 2$

Step-by-step explanation:

$\frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } = a + b \sqrt{6} \\ \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} } = a + b \sqrt{6} \\ \frac{ {( \sqrt{3} + \sqrt{2}) }^{2} }{ {( \sqrt{3} )}^{2} - {( \sqrt{2} )}^{2} } = a + b \sqrt{6} \\ \frac{3 + 2 + 2 \sqrt{6} }{3 - 2} = a + b \sqrt{6} \\ \frac{5 + 2 \sqrt{6} }{1} =a + b \sqrt{6} \\ 5 + 2 \sqrt{6} = a + b \sqrt{6} \\ a = 5 \: and \: b = 2$