Question

if a and b are rational numbers,find the value of a and b in equalities.

pls answer correctly


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Answer 1

Answer:

$\frac{ 5 + 2\sqrt{3} }{7 + 4 \sqrt{3} } = a + b \sqrt{3} \\ a + b \sqrt{3} = \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \\ = \frac{(5 + 2 \sqrt{3} ) \: (7 - 4 \sqrt{3}) }{ (7 + 4\sqrt{3} ) \: (7 - 4 \sqrt{3}) } \\ = \frac{35 - 20 \sqrt{3} + 14 \sqrt{3} - 24 }{ {7}^{2} - { (4\sqrt{3}) }^{2} } \\ = \frac{11 - 6 \sqrt{3} }{49 - 48} \\ = \frac{11 - 6 \sqrt{3} }{1} \\ a + b \sqrt{3} = 11 - 6 \sqrt{3} \\ now \: on \: comparing \\ a = 11and \: b = - 6$

Answer 2

$Answer: \: a \mapsto11 \: and \: b\mapsto \: - 6$

Step-by-step explanation:

For solving such questions multiply numerator and denominator with the number present in denominator by changing its sign or in other words rationalise the denominator

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

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

$11 - 6 \sqrt{3}$

Additional information

• always rational denominator in such questions