Solve the following equation by factorisation: 1 x + 6 + 1 x - 10 = 3 x - 4

Given, 1 x + 6 + 1 x - 10 = 3 x - 4 Taking L.C.M., we get x - 10 + x + 6 x + 6 x - 10 = 3 x - 4 ⇒ 2 x - 4 x + 6 x - 10 = 3 x - 4 ⇒ 2 x - 4 x - 4 = 3 x + 6 x - 10 ⇒ 2 x 2 - 8 x - 4 x + 16 = 3 x 2 - 4 x - 60 ⇒ 2 x 2 - 8 x - 4 x + 16 = 3 x 2 - 12 x - 180 ⇒ 2 x 2 - 8 x - 4 x + 16 - 3 x 2 + 12 x + 180 = 0 ⇒ - x 2 + 196 = 0 ⇒ x 2 - 196 = 0 ⇒ x 2 - 14 2 = 0 ⇒ x - 14 x + 14 = 0 Either x - 14 = 0 , then x = 14 or x + 14 = 0 , then x = - 14 ∴ x = 14 , - 14

Solve the following equation by factorisation: 3 x + 4 = x

Given, 3 x + 4 = x Squaring both sides, we get 3 x + 4 = x 2 ⇒ x 2 - 3 x - 4 = 0 Splitting the middle term, we get x 2 - 4 x + 1 x - 4 = 0 ⇒ x x - 4 + x - 4 = 0 ⇒ x - 4 x + 1 = 0 Either x - 4 = 0 , then x = 4 Or x + 1 = 0 , then x = - 1 ∴ x = 4 , - 1

Solve the following equation by factorisation: x x - 7 = 3 2

Given, x x - 7 = 3 2 Squaring both sides, we get x x - 7 = 18 ⇒ x 2 - 7 x = 18 ⇒ x 2 - 7 x - 18 = 0 Splitting the middle term, we get x 2 - 9 x + 2 x - 18 = 0 ⇒ x x - 9 + 2 x - 9 = 0 ⇒ x - 9 x + 2 = 0 Either x - 9 = 0 , then x = 9 Or x + 2 = 0 , then x = - 2 ∴ x = 9 , - 2

E M B I B E

Understanding ICSE Mathematics Class 10>Algebra>Chapter 5 - Quadratic Equations in One Variable>Exercise 5.2

M L Aggarwal Solutions for Exercise 2: Exercise 5.2

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Exercise 2: Exercise 5.2

Attempt the practice questions from Exercise 2: Exercise 5.2 with hints and solutions to strengthen your understanding. Understanding ICSE Mathematics Class 10 solutions are prepared by Experienced Embibe Experts.