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Symmetric Polynomial (Tomato subjective 61)

Problem: solve
\({{6x}^{2}} \) – 25x + 12 + \({\frac{25}{x}} \) + \({\frac{6}{x^2}} \) = 0.
Solution: \({{6x}^{2}} \) – 25x + 12 + \({\frac{25}{x}} \) + \({\frac{6}{x^2}} \) = 0
= 6( \({x^2} \) + \({\frac{1}{x^2}} \)) – 25(x – \({\frac{1}{x}} \)) +12 = 0
= 6 (x – \({\frac{1}{x}})^2 \) – 25 (x – \({\frac{1}{x}} \)) + 24 = 0
= (x – \({\frac{1}{x}} \)) = \({\frac{25\pm {\sqrt49}}{12}} \) = \({\frac{3}{2}} \) or \({\frac{8}{3}} \)
If (x – \({\frac{1}{x}} \)) = \({\frac{3}{2}} \)
Or \({{2x}^2} \) – 3x – 2 = 0
Or x = 2 , – \({\frac{1}{2}} \)
If (x – \({\frac{1}{x}} \)) = \({\frac{8}{3}} \)
Or \({x^2} \) – 1 = \({\frac{8}{3x}} \)
Or \({3x^2} \) – 8x – 3 = 0
Or x = 3, -1/3
X = 2,- \({\frac{1}{2}} \) ,3,- \({\frac{1}{3}} \)

June 15, 2015

8 comments

  1. What is this “latex path not specified”? How to remove this?

  2. Sir, I had mailed the screen shots of the said error of few problems. There are also other problems with this error. Please help.

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