ವಾಲ್ಮೀಕಿ ಸೀತೆಯನು ಹೇಗೆ ಸಂತೈಸುತಾನೆ?
Answers
Answer:
\begin{gathered} \\ \huge{ \underline{ \underline{ \sf{ \pmb{Question}}}}}\end{gathered}QuestionQuestion
\begin{gathered} \\ \sf{If \: x = \dfrac{ \sqrt{2a + 3b} + \sqrt{2a - 3b} }{ \sqrt{2a + 3b} - \sqrt{2a - 3b}} } \: then \: prove \: that \ratio- \end{gathered}Ifx=2a+3b−2a−3b2a+3b+2a−3bthenprovethat:−
\begin{gathered} \\ \sf{ \implies{3b {x}^{2} - 4ax + 3b = 0}}\end{gathered}⟹3bx2−4ax+3b=0
\begin{gathered} \\ \huge{ \underline{ \underline{ \sf{ \pmb{Required \: Answer}}}}}\end{gathered}RequiredAnswerRequiredAnswer
\begin{gathered} \\ \large{ \underline{ \underline{ \sf{ \pmb{Given}}}}}\end{gathered}GivenGiven
\begin{gathered} \\ \sf{x = \dfrac{ \sqrt{2a + 3b} + \sqrt{2a - 3b} }{ \sqrt{2a + 3b} - \sqrt{2a - 3b}} } \end{gathered}x=2a+3b−2a−3b2a+3b+2a−3b
\begin{gathered} \\ \large{ \underline{ \underline{ \sf{ \pmb{To \: Do}}}}}\end{gathered}ToDoToDo
\begin{gathered} \\ \sf{Prove \: that \ratio-3b {x}^{2} - 4ax + 3b = 0}\end{gathered}Provethat:−3bx2−4ax+3b=0
\begin{gathered} \\ \large{ \underline{ \underline{ \sf{ \pmb{Solution}}}}}\end{gathered}SolutionSolution
\begin{gathered} \\ \sf{ \bold{{x = \dfrac{ \sqrt{2a + 3b} + \sqrt{2a - 3b} }{ \sqrt{2a + 3b} - \sqrt{2a - 3b}}}}} \end{gathered}x=2a+3b−2a−3b2a+3b+2a−3b
By Componendo-Divinendo :-
\begin{gathered} \\ \sf{ \implies{\dfrac{x + 1}{x - 1} = \dfrac{ \sqrt{2a + 3b} + \cancel{\sqrt{2a - 3b}} + \sqrt{2a + 3b} - \cancel{ \sqrt{2a - 3b}} }{ \cancel{\sqrt{2a + 3b}} + \sqrt{2a - 3b} - \cancel{ \sqrt{2a + 3b}} + \sqrt{2a - 3b}} }}\end{gathered}⟹x−1x+1=2a+3b+2a−3b−2a+3b+2a−3b2a+3b+2a−3b+2a+3b