Question

if 2+√3/2-√3=a+b√3. find the value of a and b​

Answer 1

Question:-

$\rm \: if \: \frac{2 + \sqrt{3} }{2 - \sqrt{3} } = a \: + b \sqrt{3} \\ \rm \: find \: the \: value \: of \: a \: and \: b$

Solution:-

$\rm \: \: \frac{2 + \sqrt{3} }{2 - \sqrt{3} } = a \: + b \sqrt{3}$

Using rationalize method

$\rm \: \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} }$

Using this identity

$\rm \: (a + b) { }^{2} = {a}^{2} + {b}^{2} + 2ab$

$\rm \: (a - b)(a + b) = ( {a}^{2} + {b}^{2} )$

We get

$\rm \: \frac{(2 + \sqrt{3} ) {}^{2} }{(2) {}^{2} - ( \sqrt{3}) {}^{2} }$

$\rm \: \frac{ {2}^{2} + ( \sqrt{3}) {}^{2} + 2 \times 2 \times \sqrt{3} }{4 - 3}$

$\rm \: \frac{ {4 + 3 + 4 \sqrt{3} }}{1}$

$\rm \: 7 + 4 \sqrt{3}$

Value of a and b are

$\rm \: a = 7 \: \: \: and \: \: b \: = 4$

Answer 2

Answer:

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