Question

if 'a' and 'b' are rational numbers, find the value of a and b in each of the following equations.1)root 3+root 2 by root 3 -root 2=a+b root 6​

Answer 1

Answer:

$\large{\underline{\boxed{\sf a = 5 \: \:and \: \: b = 2}}}$

Step-by-step explanation:

Given that ;

$\sf \dfrac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } = a + b \sqrt{6}$

Consider LHS,

$\sf \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \\ \\ \sf \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2}}{ \sqrt{3} + \sqrt{2} } \\ \\ \sf \frac{( \sqrt{3} + \sqrt{2} ) {}^{2} }{( \sqrt{3})^{2} - (\sqrt{2}) {}^{2} } \\ \\ \sf \frac{( \sqrt{3}) {}^{2} + 2 \times \sqrt{3} \times \sqrt{2} + ( \sqrt{2} ) {}^{2} }{3 - 2} \\ \\ \sf \frac{3 + 2 \sqrt{6} + 2}{1} \\ \\ \sf 5 + 2 \sqrt{6}$

On comparing LHS with RHS,

$\sf 5 + 2 \sqrt{6} = a + b \sqrt{6}$

We get;

• a = 5
• b = 2

Hence, the value of a and b is 5 and 2 respectively.

Answer 2

Hey there

refer to attachment