Question

Plz help fast...............​

Answer 1

Answer:

6/7

Step-by-step explanation:

3+√2 / 3-√2 = a + b√2

= (3+√2) (3+√2) / (3-√2) (3+√2) = a + b√2

= g+6√2+2 / g-2 = a + b√2

= 11+6√2 = a + b√2

= 11/7 + 6/7√2 = a + b√2

= a = 1/7 g + b√2 = 6/7

Answer 2

Step-by-step explanation:

Question:-

Find the values of a and b if 3+√2 /3 - √2 = a + b√2

Solution:-

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

$\sf By \: rationalizing \: the \: denominator:-$

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

$\sf \dashrightarrow\dfrac{(3 + \sqrt{2})(3 + \sqrt{2} ) }{(3 - \sqrt{2} )(3 + \sqrt{2}) } = a + b \sqrt{2}$

$\sf \dashrightarrow\dfrac{(3 + \sqrt{2})^{2} }{(3) ^{2} - (\sqrt{2}) ^{2} } = a + b \sqrt{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bigg[ \because(a + b)(a - b) = { a}^{2} - {b}^{2} \bigg]$

$\sf \dashrightarrow\dfrac{ {3 }^{2} + (\sqrt{2})^{2} + 2(3)( \sqrt{2}) }{9 - 2 } = a + b \sqrt{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bigg[ \because(a + b)^{2} = { a}^{2} + {b}^{2} + 2ab \bigg]$

$\sf \dashrightarrow\dfrac{ 9 + 2 + 6 \sqrt{2} }{7} = a + b \sqrt{2}$

$\sf \dashrightarrow\dfrac{ 11 + 6 \sqrt{2} }{7} = a + b \sqrt{2}$

$\sf \dashrightarrow\dfrac{ 11 }{7} + \dfrac{6 \sqrt{2} }{7} = a + b \sqrt{2}$

$\sf Comparing \: \: \dfrac{ 11 }{7} + \dfrac{6 \sqrt{2} }{7} \: \:( with) \: \: a + b \sqrt{2}$

$\dashrightarrow \underline{ \boxed{ \sf a = \dfrac{ 11 }{7} \: \: ,\: \: b = \dfrac{6}{7}}}$