Question

√3-1/√3+1=a+b√3
explanation dena
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Answer 1

Answer:

$\mathtt\purple{❖Concept \: used:-}$

Rationalising denominator

$\mathtt\purple{❖Formula \: used:-}$

$\mathtt{(a - b)(a - b) = {a}^{2} - 2ab + {b}^{2} }$

$\mathtt{(a + b)(a - b) = {a}^{2} - {b}^{2} }$

$\mathtt\purple{❖Solution}$

$\mathtt{ = \frac{ \sqrt{3} - 1}{ \sqrt{3} + 1} \times \frac{ { \sqrt{3} } - 1}{ \sqrt{3} - 1 } }$

$\mathtt{ = \frac{( \sqrt{3})^{2} - 2 \times \sqrt{3} \times 1 + {1}^{2} }{ (\sqrt{3})^{2} - {1}^{2} } }</p><p>$

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

$\mathtt{ = \frac{4 - 2 \sqrt{3} }{2} }$

Take 2 common

$\mathtt{ = \frac{2(2 - \sqrt{3)} }{2} }$

$\mathtt\purple{ = \frac{2 - \sqrt{3} }{1} }$

$\fbox{a = 2}$

$\fbox{b = - 1}$