Question

answer this question​

Answer 1

Question :-

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

Answer :-

• a = 13
• b = 6

Step by step explanation :-

Here, first we rationalize the denominator,

$\rm:\longmapsto{ \frac{3 + \sqrt{2} }{3 - \sqrt{2} } \times \frac{3 + \sqrt{2} }{3 + \sqrt{2} } } \\ \\ \rm:\longmapsto{ \frac{(3 + \sqrt{2})(3 + \sqrt{2} )}{(3 - \sqrt{2} )(3 + \sqrt{2} )} }$

Using,

• (a+b)² = a² + 2ab + b²
• (a-b) (a+b) = a² - b²

$\rm:\longmapsto{ \frac{(3) {}^{2} + 2(3)( \sqrt{2} ) + ( \sqrt{2} ) {}^{2} }{(3) {}^{2} - ( \sqrt{2}) {}^{2} } } \\ \\ \rm:\longmapsto{ \frac{9 + 6 \sqrt{2} + 4}{3 - 2} } \: \: \: \: \: \: \: \: \ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \rm:\longmapsto \red{ \frac{13 + 6 \sqrt{2} }{1} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Taking RHS and LHS

$\rm:\longmapsto{13 + 6 \sqrt{2} = a + b \sqrt{2} }$

Comparing both sides,

${\rm:\longmapsto \red{a = 13}} \\ \\ \rm:\longmapsto \red{b = 6} \: \:$

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