Question

if a and b are rational number and 2+√3 / 2-√3 = a+b√3 find the value a and b??​

Answer 1

Step-by-step explanation:

Given:

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

To find: Value of a and b?

Solution:

Step 1: Rationalise the LHS

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

Step 2: Multiply and solve by applying identity

$( {x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy \\ \\ (x + y)(x - y) = {x}^{2} - {y}^{2}$

$\frac{( {2 + \sqrt{3}) }^{2} }{( {2)}^{2} - ( { \sqrt{3}) }^{2} } = a + b \sqrt{3} \\ \\ \frac{4 + 3 + 4 \sqrt{3} }{4 - 3} = a + b \sqrt{3} \\ \\ \frac{7 + 4 \sqrt{3} }{1} = a + b \sqrt{3}$

Step 3: Compare LHS and RHS

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

Final answer:

$a = 7 \\ \\ b = 4$

Hope it helps you.

To learn more on brainly:

5+2√3/7+4√3=a-b√3 find the value of a and b of the following

https://brainly.in/question/2547620