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JEE MainMathematicsModerateQuadratic Equations

The sum of values of x satisfying equation
2(x+1x)2=(x−1x)2+82{(x + \frac{1}{x})}^{2} = {(x - \frac{1}{x})}^{2} + 8 is

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Let
x+1x=y⇒x2+1x2=y2−2x + \frac{1}{x} = y \Rightarrow x^{2} + \frac{1}{x^{2}} = y^{2} - 2
2y2=y2−4+82y^{2} = y^{2} - 4 + 8
⇒y2=4⇒y=±2⇒x=±1\Rightarrow y^{2} = 4 \Rightarrow y = \pm 2 \Rightarrow x = \pm 1

Source: Grass-G / M-16 Mathematics Paper 25 Nov First.docx

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