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}}