Question

friends pls tell me the solution step by step pls ​

Answer 1

Step-by-step explanation:

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$\sf \dfrac{5+2 \sqrt{3}}{7+4 \sqrt{3}}\:=\:a-b \sqrt{3}$

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Value of a and b

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$\sf \dfrac{5+2 \sqrt{3}}{7+4 \sqrt{3}}\:=\:a-b \sqrt{3}$

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$\textsf{Rationalising the denominator}$

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$\sf \dfrac{5+2 \sqrt{3}}{7+4 \sqrt{3}}\times \dfrac{7-4 \sqrt{3}}{7-4 \sqrt{3}}$

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$\sf using\:identity\:(a-b)\times (a+b)\:=\:a^2-b^2$

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$\sf \dfrac{(5+2 \sqrt{3})\times (7-4 \sqrt{3})}{7^2- (4 \sqrt{3})^2}$

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$\sf \dfrac{35-20 \sqrt{3}+14 \sqrt{3}-8 \times 3}{49-48}$

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$\sf \dfrac{35-24-6\sqrt{3}}{1}$

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$\sf \:=\: 11-6\sqrt{3}$

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$\sf a\:=\:11\:,\:b\:=\:-6\sqrt{3}$

Answer 2

Question:-

Find a and b of

$\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } = a - b \sqrt{3}$

Solution:-

By the use of rationalization, we get

$\to \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} }$

Use this identity

i) ( a + b ) × ( c - d ) = (a × c - a × d + b × c - b × d )

ii) ( a - b ) ( a + b ) = ( a² - b² )

Now

$\to \: \frac{(5 + 2 \sqrt{3} )(7 - 4 \sqrt{3} )}{(7) {}^{2} - (4 \sqrt{3} ) {}^{2} }$

$\to \: \frac{35 - 20 \sqrt{3} + 14 \sqrt{3} - 8 \times 3 }{49 - 48}$

$\to \: \frac{35 - 24 - 6 \sqrt{3} }{1}$

$\to \: 11 - 6 \sqrt{3}$

Value of a = 11 and b = 6