Question

Find the value of a and b ☺️​

Answer 1

Answer:

❤️ Hey mate ❤️

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Answer 2

$\frac{1 \: + \: \sqrt{48} }{5 \sqrt{3} \: + \: 4 \sqrt{2} \: - \: \sqrt{72} \: - \: \sqrt{108} \: + \: \sqrt{8} \: + \: 2} \: = \: a \: + \: b \sqrt{3}$

___________ [ GIVEN ]

• We have to find the value of a and b.

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=> $\frac{1 \: + \: \sqrt{48} }{5 \sqrt{3} \: + \: 4 \sqrt{2} \: - \: \sqrt{72} \: - \: \sqrt{108} \: + \: \sqrt{8} \: + \: 2} \: = \: a \: + \: b \sqrt{3}$

=> $\frac{1 \: + \: 4\sqrt{3} }{5 \sqrt{3} \: + \: 4 \sqrt{2} \: - \: 6\sqrt{2} \: - \: 6\sqrt{3} \: + \: 2\sqrt{2} \: + \: 2} \: = \: a \: + \: b \sqrt{3}$

=> $\frac{1 \: + \: 4\sqrt{3} }{ - \:1 \sqrt{3} \: + \: 6 \sqrt{2} \: - \: 6\sqrt{2} \: + \: 2} \: = \: a \: + \: b \sqrt{3}$

=> $\frac{1 \: + \: 4\sqrt{3} }{ - \:1 \sqrt{3}\: + \: 2} \: = \: a \: + \: b \sqrt{3}$

On rationalization we get,

=> $\frac{(1 \: + \: 4\sqrt{3})(2 \: + \: \sqrt{3} ) }{ - \:3\: + \: 4} \: = \: a \: + \: b \sqrt{3}$

=> $(1 \: + \: 4\sqrt{3})(2 \: + \: \sqrt{3} ) \: = \: a \: + \: b \sqrt{3}$

=> $14\:+\:9\sqrt{3}\:=\:a\:+\:b\sqrt{3}$

On comparing we get,

=> a = 14 and b = 9

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