prachi happy birthday how are you where are you say me love you
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prachi happy birthday how are you where are you say me love you
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Answer:
me myself Disha
just simply I thanked u any problem
Answer :
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The required numbers are 7 and 4 or -4 and -7.
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Explanation :
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Given :
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The difference of two natural numbers is 3 & the difference of their reciprocals is 3/28.
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To Find :
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What are the numbers?
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Solution :
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Let's consider that the first number is n, As their difference is 3. Therefore the second number will be (n - 3).
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\underline{\clubsuit{\textit{\textbf{\:According\:to\:the\:Question\::}}}}♣AccordingtotheQuestion:
\begin{gathered}\\ :\implies\:\sf \dfrac{1}{n - 3} - \dfrac{1}{n} = \dfrac{3}{28}\end{gathered}:⟹n−31−n1=283
\begin{gathered}\\ \qquad:\implies\:\sf \dfrac{n - \big(n - 3\big)}{n\big(n - 3\big)} = \dfrac{3}{28}\end{gathered}:⟹n(n−3)n−(n−3)=283
\begin{gathered}\\ :\implies\:\sf \dfrac{\cancel{n} - \cancel{n} + 3}{n^2 - 3n} = \dfrac{3}{28}\end{gathered}:⟹n2−3nn−n+3=283
\begin{gathered}\\ \qquad:\implies\:\sf \dfrac{\cancel{3}}{n^2 - 3n} = \dfrac{\cancel{3}}{28}\end{gathered}:⟹n2−3n3=283
\begin{gathered}\\ :\implies\:\sf \dfrac{1}{n^2 - 3n} = \dfrac{1}{28}\end{gathered}:⟹n2−3n1=281
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By cross multiplying :
\begin{gathered}\\ \qquad:\implies\:\sf 28 = n^2 - 3n \end{gathered}:⟹28=n2−3n
\begin{gathered}\\ :\implies\:\sf n^2 - 3n - 28 = 0 \end{gathered}:⟹n2−3n−28=0
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Splitting the middle term :
\begin{gathered}\\ \qquad:\implies\:\sf n^2 - (7 - 4)n - 28 = 0 \end{gathered}:⟹n2−(7−4)n−28=0
\begin{gathered}\\ :\implies\:\sf n^2 - 7n - 4n - 28 = 0 \end{gathered}:⟹n2−7n−4n−28=0
\begin{gathered}\\ \qquad:\implies\:\sf n(n - 7) + 4(n - 7) = 0 \end{gathered}:⟹n(n−7)+4(n−7)=0
\begin{gathered}\\ :\implies\:\sf (n - 7) (n + 4) = 0 \end{gathered}:⟹(n−7)(n+4)=0
\begin{gathered}\\ \qquad:\implies\:\sf n - 7 = 0\:\:or\:\: n + 4 = 0 \end{gathered}:⟹n−7=0orn+4=0
\begin{gathered}\\ :\implies\:\sf n = 0 + 7\:\:or\:\: n = 0 - 4 \end{gathered}:⟹n=0+7orn=0−4
\begin{gathered}\\ \qquad:\implies\:\underline{\boxed{\bf{\purple{n = 7\:\:or\:\: n = -4}}}}\:\red{\clubsuit} \end{gathered}:⟹n=7orn=−4