Question

plss no spam and solve with solution
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Answer 1

Given:

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

To Find:

The value of a and b

Solution:

Let's start by simplifying the Left-Hand-Side:

$\text{LHS} = \dfrac{3 + \sqrt{2} }{3 - \sqrt{2} }$

$\text{LHS} = \dfrac{(3 + \sqrt{2}) (3 + \sqrt{2} ) }{(3 - \sqrt{3})(3 + \sqrt{2} ) }$

$\text{LHS} = \dfrac{(3 + \sqrt{2}) ^2 }{(3)^2 - (\sqrt{2})^2 }$

$\text{LHS} = \dfrac{(3 )^2+ 2(3)(\sqrt{2}) + (\sqrt{2})^2 }{(3)^2 - (\sqrt{2})^2 }$

$\text{LHS} = \dfrac{9+ 6\sqrt{2} + 2 }{9 -2 }$

$\text{LHS} = \dfrac{11+ 6\sqrt{2} }{7}$

$\text{LHS} = \dfrac{11}{7} + \dfrac{6}{7}\sqrt{2}$

Now, we compare the LHS and the RHS:

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

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

Therefore:

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

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

$\boxed{\text{Answer : } a = \frac{11}{7} , b = \dfrac{6}{7} }$

Answer 2

Hello here's your answer:( 11÷ 7 )- (6root2÷7)

If you have any doubt than comment me.

Hope you be happy with this answer.

: ) : ) . . . . . . . . . . . . . .