Question

Find a and b if 3+root 2 /3-root2=a+b root 2​

Answer 1

Answer:

Hey mate....❤❤

Here is your answer.....

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

Take L.H.S

Now rationalise the denominator

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

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

$\frac{9 + 2 + 2(3)( \sqrt{2)} }{9 - 2}$

$\frac{11 + 6 \sqrt{2} }{7}$

We can also write it as -

$\frac{11}{7} + \frac{6}{7} \sqrt{2}$

Compare it with the R.H.S

$\frac{11}{7} + \frac{6 \sqrt{2} }{7} = a + b \sqrt{2}$

Acoording to this equation ;

$a = \frac{11}{7}$

and

$b = \frac{6 }{7}$

Please mark it the brainliest answer