Question

2+√3/2-√3=a+b√3
please tell me​

Answer 1

Step-by-step explanation:

Question:-

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

To find:-

The value of a + b√3

Solution:-

Let's solve the given problem

We have,

$\frac{2 + \sqrt{3} }{2 - \sqrt{3} }$

The denominator is 2-√3. Multiplying the numerator and denomination by 2+√3, we get

$⟹ \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} }$

$⟹ \frac{(2 + \sqrt{3})(2 + \sqrt{3} )}{(2 - \sqrt{3} )(2 + \sqrt{3} )}$

⬤ Applying Algebraic Identity

• (a+b)(a+b) = (a+b)² = a²+b²+2ab to the numerator &
• (a-b)(a+b) = a² - b² to the denominator

We get,

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

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

$⟹ \frac{4 + \sqrt{3} + 4 \sqrt{3} }{1}$

$⟹ \frac{7 + 4 \sqrt{3} }{1}$

$⟹7 + 4 \sqrt{3}$

$∴ \: a + b \sqrt{3} = 7 + 4 \sqrt{3}$

On comparing, the value of:

$\mathrm{a = 7 \: \: and \: \: b = 4}$

Answer:-

$\mathrm{Hence, \: the \: value \: of \: a = 7 \: \: and \: \: b = 4.}$

Used Formulae:-

• (a+b)(a+b) = (a+b)² = a² + b² +2ab

• (a-b)(a+b) = a² - b²

:)