Question

if 5+4 root 3/5+4 root3=a-b root 3, find a and b.please answer it immediatly.it is urjent​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Value\:of\:a=5}}}$

$\green{\tt{\therefore{Value\:of\:b=-\frac{24}{5}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies 5 + \frac{4 \sqrt{3} }{ 5} + 4 \sqrt{3} = a - b \sqrt{3} \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Value \: of \: a =? \\ \\ \tt: \implies Value \: of \: b =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies 5 + \frac{4 \sqrt{3} }{5} + 4 \sqrt{3} = a - b \sqrt{3} \\ \\ \tt: \implies \frac{5 \times 5 + 4 \sqrt{3} + 4 \times 5\sqrt{3} }{5} = a - b \sqrt{3} \\ \\ \tt: \implies \frac{25 + 4 \sqrt{3} + 20 \sqrt{3} }{5} = a - b \sqrt{3} \\ \\ \tt: \implies \frac{25 + 24 \sqrt{3} }{5} = a - b \sqrt{3} \\ \\ \tt: \implies \frac{25}{5} + \frac{24 \sqrt{3} }{5} = a - b \sqrt{3} \\ \\ \text{Both \: side \: comparing :} \\ \green{\tt: \implies a = \frac{25}{5} = 5} \\ \\ \tt: \implies - b \sqrt{3} = \frac{24 \sqrt{3} }{5} \\ \\ \tt: \implies b = - \frac{24 \sqrt{3} }{5 \sqrt{3} } \\ \\ \green{\tt: \implies b = - \frac{ 24}{5} }$

Answer 2

✪ CorrecT QuestioN ✪

$\tt{If\ \dfrac{5+4\sqrt{3} }{5-4\sqrt{3} }=a-b\sqrt{3},\ find\ the\ value\ of\ a\ and\ b.}$

✪ SolutioN ✪

$\tt{Rationalising\:\: \dfrac{5+4\sqrt{3}}{5-4\sqrt{3}}:- }$

$\tt{\dfrac{5+4\sqrt{3} }{5-4\sqrt{3} } }\\\\\\\tt{=\dfrac{(5+4\sqrt{3})(5+4\sqrt{3})}{(5-4\sqrt{3})(5+4\sqrt{3})} }\\\\\\\tt{=\dfrac{(5+4\sqrt{3})^2}{(5)^2-(4\sqrt{3})^2}}\\\\\\\tt{=\dfrac{(5)^2+(4\sqrt{3})^2-2\times5\times4\sqrt{3}}{25-48}}\\\\\\\tt{=\dfrac{25+48-40\sqrt{3}}{-23} }\\\\\\\tt{=\dfrac{-(73-40\sqrt{3})}{23}}\\\\\\\tt{=\dfrac{-73+40\sqrt{3}}{23}}$

$\tt{=\dfrac{-73}{23}+\dfrac{40\sqrt{3}}{23} }\\\\\\\tt{\implies \dfrac{-73}{23}+\dfrac{40\sqrt{3}}{23}=a-b\sqrt{3} }$

On comparing,

$\boxed{\tt{a=\dfrac{-73}{23}}\:\:\:\:and\:\:\:\:b=\dfrac{40}{23}}$