Question

find the value of (a) and (b) -
$\frac{6}{3 \sqrt{2} + 2 \sqrt{3} } + \frac{6}{3 \sqrt{2} - 2 \sqrt{3} } = a \sqrt{2} + b$
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Answer 1

To Find :

The value of 'a' and 'b' fro. the given equation.

Given :

The equation Given is :

$\tt{\frac{6}{3 \sqrt{2} + 2 \sqrt{3} } + \frac{6}{3 \sqrt{2} - 2 \sqrt{3} } = a \sqrt{2} + b}$

Process :

First we will find the RF of the given terms in the LHS, then we will rationalise the denominator. Now, we will simply the answer to get the Same format of constants as in RHS.

Solution :

$\tt{rf \: of \: \frac{6}{3 \sqrt{2} + 2\sqrt{3} } = \frac{3 \sqrt{2} - 2 \sqrt{3} }{3 \sqrt{2} - 2 \sqrt{3} } }$

$\implies \tt{ \frac{6}{3 \sqrt{2} + 2\sqrt{3} } \times \frac{3 \sqrt{2} - 2 \sqrt{3} }{3 \sqrt{2} - 2 \sqrt{3} } }$

$\implies \tt{ \frac{6(3 \sqrt{2} - 2 \sqrt{3}) }{(3 \sqrt{2} {)}^{2} - (2 \sqrt{3} {)}^{2} } }$

$\implies \tt{ \frac{6(3 \sqrt{2} - 2 \sqrt{3} )}{18 - 12} }$

$\implies \tt{ \frac{6(3 \sqrt{2} - 2 \sqrt{3} )}{6} }$

$\implies \tt{3 \sqrt{2} - 2 \sqrt{3}}$

Hence,

$\tt{ \frac{6}{3 \sqrt{2} + 2 \sqrt{3} } = 3 \sqrt{2} - 2 \sqrt{3}}$

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Now,

$\tt{rf \: of \: \frac{6}{3 \sqrt{2} - 2 \sqrt{3} } = \frac{ 3\sqrt{2} + 2\sqrt{3} }{3\sqrt{2} + 2\sqrt{3} } }$

$\implies \tt{ \frac{6}{2 \sqrt{3} - 3 \sqrt{2} } \times \frac{3 \sqrt{2} + 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} } }$

$\implies \tt{ \frac{6(3 \sqrt{2} + 2 \sqrt{3} )}{(3 \sqrt{2} {)}^{2} - (2 \sqrt{3} {)}^{2} } }$

$\tt{ \implies \frac{6(3 \sqrt{2} + 2 \sqrt{3} }{6} }$

$\implies \tt{ \frac{6}{3 \sqrt{2} - 2 \sqrt{3} } = 2 \sqrt{3} + 3 \sqrt{2} }$

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So, now the sum :

$\tt{ \frac{6}{3 \sqrt{2} + 2 \sqrt{3} } + \frac{6}{3 \sqrt{2} - 2 \sqrt{3} } = a \sqrt{2} + b}$

$\tt{\implies(3 \sqrt{2} - 2 \sqrt{3} ) + (3 \sqrt{2} + 2 \sqrt{3} ) = a \sqrt{2} + b }$

$\implies \tt{3 \sqrt{2} + 0 = a \sqrt{2} + b}$

Hence, most probably:

• a = 3
• b = 0

Answer 2

Answer:

first we multiply the numerator & denominator by (3√2+2√3) then we use formula in the denominator = a+b)(a-b) = a^2-b&2

The value of a= 2 & b= -5/6

Explanation:

heya!

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