Question

3/root3-root2 = a roit3 - b root2​

Answer 1

Answer:

$a = 3$

$b = - 3$

Step-by-step explanation:

$\frac{3}{ \sqrt{3} - \sqrt{2} } = a \sqrt{3} - b \sqrt{2}$

Rationalising the denominator, we get

$= \frac{3}{ \sqrt{ 3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} }$

$= \frac{3( \sqrt{3} + \sqrt{2} )}{( \sqrt{3} - \sqrt{2} )( \sqrt{3} + \sqrt{2} )}$

$= \frac{3 \sqrt{3} + 3 \sqrt{2} }{ { (\sqrt{3} )}^{2} - {( \sqrt{2}) }^{2} }$

$= \frac{3 \sqrt{3} + 3 \sqrt{2} }{3 - 2}$

$= \frac{3 \sqrt{3} + 3 \sqrt{2} }{1}$

$= 3 \sqrt{3} + 3 \sqrt{2}$

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

$a \sqrt{3} = 3 \sqrt{3} \: \: \: \: \: \: \: \: - b \sqrt{2} = 3 \sqrt{2}$

$a = 3 \: \: \: \: \: \: \: b = - 3$

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Answer 2

Answer:

Step-by-step explanation:

\frac{3}{ \sqrt{3} - \sqrt{2} } = a \sqrt{3} - b \sqrt{2}3−23=a3−b2

Rationalising the denominator, we get

= \frac{3}{ \sqrt{ 3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} }=3−23×3+23+2

= \frac{3( \sqrt{3} + \sqrt{2} )}{( \sqrt{3} - \sqrt{2} )( \sqrt{3} + \sqrt{2} )}=(3−2)(3+2)3(3+2)

= \frac{3 \sqrt{3} + 3 \sqrt{2} }{ { (\sqrt{3} )}^{2} - {( \sqrt{2}) }^{2} }=(3)2−(2)233+32

= \frac{3 \sqrt{3} + 3 \sqrt{2} }{3 - 2}=3−233+32

= \frac{3 \sqrt{3} + 3 \sqrt{2} }{1}=133+32

= 3 \sqrt{3} + 3 \sqrt{2}=33+32

3 \sqrt{3} + 3 \sqrt{2} = a \sqrt{3} - b \sqrt{2}33+32=a3−b2

a \sqrt{3} = 3 \sqrt{3} \: \: \: \: \: \: \: \: - b \sqrt{2} = 3 \sqrt{2}a3=33−b2=32