Determine a and b if 5- 3 7-4- 3 -94a-3- 3 b

5+√(3)7 4√(3)=5+√(3)7 4√(3).7+4√(3)7+4√(3) =47+27√(3)1=94a+3√(3)b a=4794,b=9 ...

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Standard VI

Mathematics

Addition of Fractions

Determine a...

Question

Determine $a$ and $b$ if $\frac{5 + \sqrt{3}}{7 - 4 \sqrt{3}} = 94 a + 3 \sqrt{3} b$

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Solution

$\frac{5 + \sqrt{3}}{7 - 4 \sqrt{3}} = \frac{5 + \sqrt{3}}{7 - 4 \sqrt{3}} . \frac{7 + 4 \sqrt{3}}{7 + 4 \sqrt{3}}$
$= \frac{47 + 27 \sqrt{3}}{1} = 94 a + 3 \sqrt{3} b$
$a = \frac{47}{94}, b = 9$

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Q. The value of a if

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(iv) $\frac{5 + 3 \sqrt{3}}{7 + 4 \sqrt{3}} = a + b \sqrt{3}$

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If a and b are rational numbers, find 'a' and 'b' when

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Determine a and b if 5+√37−4√3=94a+3√3b

5+√37−4√3=5+√37−4√3.7+4√37+4√3=47+27√31=94a+3√3ba=4794,b=9

Determine $a$ and $b$ if $\frac{5 + \sqrt{3}}{7 - 4 \sqrt{3}} = 94 a + 3 \sqrt{3} b$

$\frac{5 + \sqrt{3}}{7 - 4 \sqrt{3}} = \frac{5 + \sqrt{3}}{7 - 4 \sqrt{3}} . \frac{7 + 4 \sqrt{3}}{7 + 4 \sqrt{3}}$
$= \frac{47 + 27 \sqrt{3}}{1} = 94 a + 3 \sqrt{3} b$
$a = \frac{47}{94}, b = 9$