Question

please answer this ​

Answer 1

Answer :

Step-by-step explanation: hey mate hope this helps you. Please mark me as brainliest.

Answer 2

$\huge{\frak{\underline{\underline{\:ANSWER}}}}$

$\large\sf{\underline{\:Given}}$

$\mapsto\pink{\sf{\:\left(\dfrac{1+\sqrt{3}}{1-\sqrt{3}}\right)\:=\:A+B\sqrt{3}}}$

$\large\sf{\underline{\:Find}}$

$\mapsto\pink{\sf{\:Value\:Of\:A\:and\:B}}$

$\huge{\frak{\underline{\underline{\:ExplanaTiOn}}}}$

$\pink{\sf{\:\left(\dfrac{1+\sqrt{3}}{1-\sqrt{3}}\right)\:=\:A+B\sqrt{3}}}$

$\:\:\:\:\:\:\:\green{\textsf{\small{\:(Rationalization Of Denominator) }}}$

$\mapsto\sf{\:\left(\dfrac{1+\sqrt{3}}{1-\sqrt{3}}\right)\:\times\left(\dfrac{1+\sqrt{3}}{1+\sqrt{3}}\right)\:=\:A+B\sqrt{3}}$

$\mapsto\sf{\:\left(\dfrac{1^2+(\sqrt{3})^2+2\times\sqrt{3}}{1^2-(\sqrt{3})^2}\right)\:=\:A+B\sqrt{3}}$

$\mapsto\sf{\:\left(\dfrac{1+3+2\sqrt{3}}{1-3}\right)\:=\:A+B\sqrt{3}}$

$\mapsto\sf{\:\left(\dfrac{4+2\sqrt{3}}{-2}\right)\:=\:A+B\sqrt{3}}$

$\:\:\:\:\:\:\:\green{\textsf{\small{\:(Take 2 common ) }}}$

$\mapsto\sf{\:\left(\dfrac{\cancel{2}(2+\sqrt{3})}{-\cancel{2}}\right)\:=\:A+B\sqrt{3}}$

$\mapsto\sf{\:\left(2-\sqrt{3}\right)\:=\:A+B\sqrt{3}}$

$\:\:\:\:\:\:\:\green{\textsf{\small{\:(Compare both side ) }}}$

$\Large\sf{\underline{\underline{\:Value\:of\:A\:and\:B}}}$

$\mapsto\orange{\textsf{\:Value of A = 2}}$

$\mapsto\orange{\textsf{\:Value of B = -1}}$

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