Question

under root 3 + 1 divided by under root 3 minus 1 is equals to a + b under root 3 find the value of

Answer 1

........ ...... . .

Answer 2

Complete question is "under root 3 + 1 divided by under root 3 minus 1 is equals to a + b under root 3 find the value of a and b".

Answer:

Required value of a is 2 and b is 1.

Step-by-step explanation:

Given,under root 3 + 1 divided by under root 3 minus 1 is equals to a + b under root 3

Or,

$\frac{ \sqrt{3} + 1}{ \sqrt{3} - 1 } = a + 3 \sqrt{b}$

Now,

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

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

Comparing both side and get,

$a = 2 \\ b = 1$

This is a problem of Power of indices .

Some important formulas of Power of indices:

${x}^{0} = 1 \\ {x}^{1} = x \\ {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ {x}^{ {y}^{a} } = {x}^{ya} \\ {x}^{ - 1} = \frac{1}{x} \\ {x}^{a} \times {y}^{a} = {(xy)}^{a}$

Power of indices related two more questions:

https://brainly.in/question/20611233

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