Question

Find the values of a and b in( 5+2√3)/(7+4√3)= a+b√3​

Answer 1

Step-by-step explanation:

by rationalising their denominator

a=11

b= -6

Answer 2

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

Or,

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

Or,

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

Or,

$\frac{35 - 20 \sqrt{3} + 14 \sqrt{3} - 24}{49 - 48} = a + b \sqrt{3}$

Or,

$35 - 24 - 20 \sqrt{3} + 14 \sqrt{3} = a + b \sqrt{3}$

Or,

$11 - 6 \sqrt{3} = a + b \sqrt{3}$

Comparing both side, we get,

$a = 11$

$b = - 6$

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