Question

Find rational number a and b


$please \: help \:$
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Answer 1

Answer:

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

Rationalising the denominator...

We will multiply both the denominator and numerator by √3-1 ....

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

Using the formula.... (a-b)^2 = a^2 + b^2 -2ab

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

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

1- √3 = a +b √3

Therefore a= 1 and b = -1

Hope it helps you...........

If you still have any doubts then you can comment....