(a−b)2−(a+b)2−4a = xy(a−b)2−(a+b)2−4a = xy\frac{{{{\left( {a - b} \right)}^2} - {{\left( {a + b} \right)}^2}}}{{ - 4a}}{\text{ = }}\frac{x}{y} On simplifying the given equations, which of the following equations will be obtained ? " /> (a−b)2−(a+b)2−4a = xy(a−b)2−(a+b)2−4a = xy\frac{{{{\left( {a - b} \right)}^2} - {{\left( {a + b} \right)}^2}}}{{ - 4a}}{\text{ = }}\frac{x}{y} On simplifying the given equations, which of the following equations will be obtained ? " /> (a−b)2−(a+b)2−4a = xy(a−b)2−(a+b)2−4a = xy\frac{{{{\left( {a - b} \right)}^2} - {{\left( {a + b} \right)}^2}}}{{ - 4a}}{\text{ = }}\frac{x}{y} On simplifying the given equations, which of the following equations will be obtained ? " />

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$\frac{{(a - b)}^{2} - {(a + b)}^{2}}{- 4 a} = \frac{x}{y}$ $\frac{{{{\left( {a - b} \right)}^2} - {{\left( {a + b} \right)}^2}}}{{ - 4a}}{\text{ = }}\frac{x}{y}$ On simplifying the given equations, which of the following equations will be obtained ?

1xy = b
2bx = y
3ab = x
4yb = x

Answer:- 4

Explanation:-

Solution:

\begin{aligned} \frac{{(a - b)}^{2} - {(a + b)}^{2}}{- 4 a} = \frac{x}{y} \\ \Rightarrow \frac{(a^{2} + b^{2} - 2 a b) - (a^{2} + b^{2} + 2 a b)}{- 4 a} = \frac{x}{y} \\ \Rightarrow \frac{- 4 a b}{- 4 a} = \frac{x}{y} \\ \Rightarrow b = \frac{x}{y} \\ \Rightarrow x = y b . \end{aligned}

$\eqalign{ & \frac{{{{\left( {a - b} \right)}^2} - {{\left( {a + b} \right)}^2}}}{{ - 4a}}{\text{ = }}\frac{x}{y} \cr & \Rightarrow \frac{{\left( {{a^2} + {b^2} - 2ab} \right) - \left( {{a^2} + {b^2} + 2ab} \right)}}{{ - 4a}} = \frac{x}{y} \cr & \Rightarrow \frac{{ - 4ab}}{{ - 4a}} = \frac{x}{y} \cr & \Rightarrow b = \frac{x}{y} \cr & \Rightarrow x = yb. \cr}$

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On simplifying the given equations, which of the following equations will be obtained ? ", "text": "

\frac{{(a - b)}^{2} - {(a + b)}^{2}}{- 4 a} = \frac{x}{y}

$\frac{{{{\left( {a - b} \right)}^2} - {{\left( {a + b} \right)}^2}}}{{ - 4a}}{\text{ = }}\frac{x}{y}$ On simplifying the given equations, which of the following equations will be obtained ? ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} \frac{{(a - b)}^{2} - {(a + b)}^{2}}{- 4 a} = \frac{x}{y} \\ \Rightarrow \frac{(a^{2} + b^{2} - 2 a b) - (a^{2} + b^{2} + 2 a b)}{- 4 a} = \frac{x}{y} \\ \Rightarrow \frac{- 4 a b}{- 4 a} = \frac{x}{y} \\ \Rightarrow b = \frac{x}{y} \\ \Rightarrow x = y b . \end{aligned}

$\eqalign{ & \frac{{{{\left( {a - b} \right)}^2} - {{\left( {a + b} \right)}^2}}}{{ - 4a}}{\text{ = }}\frac{x}{y} \cr & \Rightarrow \frac{{\left( {{a^2} + {b^2} - 2ab} \right) - \left( {{a^2} + {b^2} + 2ab} \right)}}{{ - 4a}} = \frac{x}{y} \cr & \Rightarrow \frac{{ - 4ab}}{{ - 4a}} = \frac{x}{y} \cr & \Rightarrow b = \frac{x}{y} \cr & \Rightarrow x = yb. \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} \frac{{(a - b)}^{2} - {(a + b)}^{2}}{- 4 a} = \frac{x}{y} \\ \Rightarrow \frac{(a^{2} + b^{2} - 2 a b) - (a^{2} + b^{2} + 2 a b)}{- 4 a} = \frac{x}{y} \\ \Rightarrow \frac{- 4 a b}{- 4 a} = \frac{x}{y} \\ \Rightarrow b = \frac{x}{y} \\ \Rightarrow x = y b . \end{aligned}

$\eqalign{ & \frac{{{{\left( {a - b} \right)}^2} - {{\left( {a + b} \right)}^2}}}{{ - 4a}}{\text{ = }}\frac{x}{y} \cr & \Rightarrow \frac{{\left( {{a^2} + {b^2} - 2ab} \right) - \left( {{a^2} + {b^2} + 2ab} \right)}}{{ - 4a}} = \frac{x}{y} \cr & \Rightarrow \frac{{ - 4ab}}{{ - 4a}} = \frac{x}{y} \cr & \Rightarrow b = \frac{x}{y} \cr & \Rightarrow x = yb. \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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