Question

if $\frac{2+√3}{2-√3}$ =a+b√3 then find the values of a and b​

Answer 1

Answer:

4-3=a+b√3

1=a+b√3

on compairing

a=1

b=o

Step-by-step explanation:

are the answers of this question

Answer 2

Answer:

$\frac{2 + \sqrt{3} }{2 - \sqrt{3} } = a + b \sqrt{3} \\ l \: h \:s = \frac{2 + \sqrt{3} }{2 - \sqrt[]{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } \\ = \frac{ ({2 + \sqrt{3}) }^{2} }{ {(2)}^{2} - {( \sqrt{3}) }^{2} } \\ = \frac{4 + 4\sqrt{3} + 3}{4 - 3} \\ = 7 + 4\sqrt{3}$

Now comparing L.H.S and R.H.S

We get,

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

therefore here,

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

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