Question

pls solve this is urgent 20 points

Answer 1

Step-by-step explanation:

Hope the ans may helpful to you

Answer 2

$\LARGE\star\boxed{\mathfrak\pink{\underline{\underline{Answer}}}}\star$

$\Large\textbf{a\: = \: \dfrac{-61}{9} \: ,\:b\: =\: \dfrac{-24}{29} }$

$\Large\textbf{\:or \:Option\:B}$

$\LARGE\star\star\boxed{\mathbb\red{\underline{\underline{GIVEN}}}}\star\star$

$\Large\odot\:\:\textbf{ \dfrac{4+3\sqrt{5}}{4-3\sqrt{5}} \:=\: a+b\sqrt{5} }$

$\LARGE\star\star\star\boxed{\mathbb\green{\underline{\underline{TO\:FIND}}}}\star\star\star$

$\Large\odot\:\:\textbf{Value\:of\:a\:and\:b}$

$\LARGE\star\star\star\boxed{\mathcal\red{\underline{\underline{Explanation}}}}\star\star\star$

$\large\odot\:\:\textsf{ \dfrac{4+3\sqrt{5}}{4-3\sqrt{5}} \:=\: a+b\sqrt{5} }$

$\Large\texttt{Rationalising the}$

$\Large\texttt{fraction by multiplying}$

$\Large\texttt{numerator and denominator}$

$\Large\texttt{by 4+3\sqrt{5} }$

$\large\Longrightarrow\textsf{ \dfrac{4+3\sqrt{5}}{4-3\sqrt{5}}\times\dfrac{4+3\sqrt{5}}{4+3\sqrt{5}} \:=\: a+b\sqrt{5} }$

$\large\Longrightarrow\textsf{ \dfrac{(4+3\sqrt{5})^2}{4^2-(3\sqrt{5})^2} = a+b \sqrt{5} }$

$\large\Longrightarrow\textsf{ \dfrac{16+45+24\sqrt{5}}{16-45} = a+ b\sqrt{5} }$

$\large\Longrightarrow\textsf{ \dfrac{61+24\sqrt{5}}{-29} = a+ b\sqrt{5} }$

$\Large\texttt{The above fraction can be}$

$\Large\texttt{written as below fraction}$

$\large\Longrightarrow\textsf{ \dfrac{-61}{29}+\dfrac{-24\sqrt{5}}{29} = a+ b\sqrt{5} }$

$\Large\texttt{Comparing the values of a}$

$\Large\texttt{and b on both sides,}$

$\Large\texttt{we get}$

$\Large\therefore\textsf{The Answer is a = \dfrac{-61}{29} and }$

$\Large\textsf{b = \dfrac{-24}{29} or Option B.}$

$\Huge\mathcal{Note}$

$\large\odot\:\:\texttt{In such types of }$

$\large\texttt{questions, we first}$

$\large\texttt{rationalise the denominator}$

$\large\texttt{of the fraction by}$

$\large\texttt{multiplying the fraction}$

$\large\texttt{with numerator. This is}$

$\large\texttt{called Rationalising and}$

$\large\texttt{the number that is }$

$\large\texttt{multiplied is called the}$

$\large\texttt{rationalising factor.}$

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