# 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,- $${\frac{1}{3}}$$

## 8 Replies to “Symmetric Polynomial (Tomato subjective 61)”

1. Sir, It is showing in the problem and in the entire solution as well. “Problem: solve
latex path not specified– 25x + 12 + latex path not specified + latex path not specified = 0.”

1. Sir, I am having this problem with subjective 57, 58, 125, 124, 67, 128, 127 among the recent posts. Due to this problem I am unable to understand the solution and solve the problem. If I get a mail-id I can provide the screen shot of the error. Please help.

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