Question

solution of relation equation of 6_4√2/6+4√2​

Answer 1

Answer:

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Answer 2

Question:-

Solution of relation equation of

$\frac{6 - 4 \sqrt{2} }{6 + 4 \sqrt{2} }$

Solution:-

We can solve this by rationalising the equation

We have to multiply both numerator with 6-4√2

So,

$\frac{6 - 4 \sqrt{2} }{6 + 4 \sqrt{2} } \times \frac{6 - 4 \sqrt{2} }{6 - 4 \sqrt{2} }$

$= > \frac{(6 - 4 \sqrt{2})(6 - 4 \sqrt{2} ) }{(6 + 4 \sqrt{2})(6 - 4 \sqrt{2} ) }$

We have

$(a + b)(a - b) = {a}^{2} - {b}^{2}$

So,

$\frac{ ({6 - 4 \sqrt{2} )}^{2} }{ {(6)}^{2} - {(4 \sqrt{2} )}^{2} }$

We have,

${(a - b)}^{2} = {a}^{2} + {b}^{2} - 2 \times a\times \: b$

So,

$\frac{( {6}^{2}) - 2 \times 6 \times 4 \sqrt{2} + ( {4 \sqrt{2} )}^{2} }{36 - (16 \times 2)}$

$\frac{36 - 48 \sqrt{2} + 32 }{36 - 32}$

$\frac{48 - 48 \sqrt{2} }{4}$

$\frac{4(12 - 12 \sqrt{2} )}{4}$

$= > 12 - 12 \sqrt{2}$