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If x + 1/x = 12 find the value of x – 1/x. |
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Answer» We know that x + 1/x = 12 So when squaring both sides, we get (x + 1/x)2 = (12)2 x2 + 2 × x × 1/x + (1/x)2 = 144 x2 + 2 + 1/x2 = 144 x2 + 1/x2 = 144 – 2 x2 + 1/x2 = 142 When subtracting 2 from both sides, we get x2 + 1/x2 – 2 × x × 1/x = 142 – 2 (x – 1/x)2 = 140 x – 1/x = √140 |
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