Question

if :
$\frac{3}{ \sqrt{2} } = a + b \sqrt{2}$
then find the values of a and b
​

Answer 1

$a = 0 \: \: \: and \: \: \: b = \frac{3}{2}$

Step-by-step explanation:

$Given, \: \: \: \frac{3}{ \sqrt{2} } = a + b \sqrt{2} \\ \: \: \: \: \: \: \: \: \: \: = > \: \: \frac{3}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } = a + b\sqrt{2} \\ = > \: \: \frac{3 \sqrt{2} }{2} = a + b \sqrt{2} \\ \: \: \: \: \: \: \: \: = > \: \: 0 + \frac{3}{2} \sqrt{2} = a + b \sqrt{2} \\ By \: \: comparison, \\ then, \: \: a = 0 \: \: \: and \: \: \: b = \frac{3}{2}$

Answer 2

Step-by-step explanation:

Given,

2

3

=a+b

2

=>

2

3

×

2

2

=a+b

2

=>

2

3

2

=a+b

2

=>0+

2

3

2

=a+b

2

Bycomparison,

then,a=0andb=

2

3