Solve the equation by factorisation: 1 x - 1 x - 2 + 1 x - 2 x - 3 + 1 x - 3 x - 4 = 1 6 .

The given equation is: 1 x - 1 x - 2 + 1 x - 2 x - 3 + 1 x - 3 x - 4 = 1 6 Taking LCM of denominators in the LHS, we get x - 3 x - 4 + x - 1 x - 4 + x - 1 x - 2 x - 1 x - 2 x - 3 x - 4 = 1 6 ⇒ x - 3 x - 4 + x - 1 x - 4 + x - 2 x - 1 x - 2 x - 3 x - 4 = 1 6 ⇒ x - 3 x - 4 + x - 1 2 x - 6 x - 1 x - 2 x - 3 x - 4 = 1 6 ⇒ x - 3 x - 4 + x - 1 2 x - 3 x - 1 x - 2 x - 3 x - 4 = 1 6 ⇒ x - 3 x - 4 + 2 x - 2 x - 1 x - 2 x - 3 x - 4 = 1 6 ⇒ x - 3 3 x - 6 x - 1 x - 2 x - 3 x - 4 = 1 6 ⇒ x - 3 3 x - 2 x - 1 x - 2 x - 3 x - 4 = 1 6 ⇒ 3 x - 1 x - 4 = 1 6 ⇒ x - 1 x - 4 = 18 ⇒ x 2 - 4 x - x + 4 = 18 ⇒ x 2 - 5 x - 14 = 0 Factorising the above equation by splitting the middle term, we get ⇒ x 2 - 7 x + 2 x - 14 = 0 ⇒ x x - 7 + 2 x - 7 = 0 ⇒ x + 2 x - 7 = 0 ⇒ x + 2 = 0 or x - 7 = 0 ⇒ x = - 2 or x = 7 Hence, x = - 2 and x = 7 are the roots of the given equation.

E M B I B E

Modern's abc+ of Mathematics for Class 10>Chapter 4 - Quadratic Equations>EXERCISE

J P Mohindru and Bharat Mohindru Solutions for Chapter: Quadratic Equations, Exercise 3: EXERCISE

Author:J P Mohindru & Bharat Mohindru

J P Mohindru Mathematics Solutions for Exercise - J P Mohindru and Bharat Mohindru Solutions for Chapter: Quadratic Equations, Exercise 3: EXERCISE

Attempt the free practice questions on Chapter 4: Quadratic Equations, Exercise 3: EXERCISE with hints and solutions to strengthen your understanding. Modern's abc+ of Mathematics for Class 10 solutions are prepared by Experienced Embibe Experts.