Solve :
2800x−100−2800x=12\dfrac{2800}{x - 100} - \dfrac{2800}{x} = \dfrac{1}{2}x−1002800−x2800=21
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⇒2800x−100−2800x=12⇒2800x−2800(x−100)x(x−100)=12⇒2800x−2800x+280000x2−100x=12⇒2(280000)=x2−100x⇒560000=x2−100x⇒x2−100x−560000=0⇒x2−800x+700x−560000=0⇒x(x−800)+700(x−800)=0⇒(x+700)(x−800)=0⇒x=−700 or x=800\Rightarrow \dfrac{2800}{x - 100} - \dfrac{2800}{x} = \dfrac{1}{2} \\[1em] \Rightarrow \dfrac{2800x - 2800(x - 100)}{x(x - 100)} = \dfrac{1}{2} \\[1em] \Rightarrow \dfrac{2800x - 2800x + 280000}{x^2 - 100x} = \dfrac{1}{2} \\[1em] \Rightarrow 2(280000) = x^2 - 100x \\[1em] \Rightarrow 560000 = x^2 - 100x \\[1em] \Rightarrow x^2 - 100x - 560000 = 0 \\[1em] \Rightarrow x^2 - 800x + 700x - 560000 = 0 \\[1em] \Rightarrow x(x - 800) + 700(x - 800) = 0 \\[1em] \Rightarrow (x + 700)(x - 800) = 0 \\[1em] \Rightarrow x = -700 \text { or } x = 800⇒x−1002800−x2800=21⇒x(x−100)2800x−2800(x−100)=21⇒x2−100x2800x−2800x+280000=21⇒2(280000)=x2−100x⇒560000=x2−100x⇒x2−100x−560000=0⇒x2−800x+700x−560000=0⇒x(x−800)+700(x−800)=0⇒(x+700)(x−800)=0⇒x=−700 or x=800
Hence, x = 800.
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