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Test of Mathematics Solution Subjective 61 - Symmetric Polynomial

Test of Mathematics at the 10+2 Level

This is a Test of Mathematics Solution Subjective 61 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.


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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}} $

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