Solve the following equations. 2 x + 1 2 + 2 x - 1 2 2 x + 1 2 - 2 x - 1 2 = 17 8

Given: 2 x + 1 2 + 2 x - 1 2 2 x + 1 2 - 2 x - 1 2 = 17 8 We first put x = 0 in the expression and obtain: 2 0 + 1 2 + 2 0 - 1 2 2 0 + 1 2 - 2 0 - 1 2 = 17 8 ⇒ 1 + 1 1 - 1 = 17 8 ⇒ 2 0 = 17 8 which does not hold true. ∴ x = 0 is not a solution. Now, Consider : 2 x + 1 2 + 2 x - 1 2 2 x + 1 2 - 2 x - 1 2 = 17 8 Apply componendo and dividendo: 2 x + 1 2 + 2 x - 1 2 + [ 2 x + 1 2 - 2 x - 1 2 ] 2 x + 1 2 + 2 x - 1 2 - [ 2 x + 1 2 - 2 x - 1 2 ] = 17 + 8 17 - 8 ⇒ 2 x + 1 2 x - 1 2 = 25 9 ⇒ 2 x + 1 2 x - 1 = ± 5 3 Case I: If 2 x + 1 2 x - 1 = 5 3 6 x + 3 = 10 x – 5 ⇒ 4 x = 8 ⇒ x = 2 Case II: If 2 x + 1 2 x - 1 = - 5 3 6 x + 3 = - 10 x + 5 ⇒ 16 x = 2 ⇒ x = 1 8 &there4; x = 2 , 1 8 are the solutions.

Solve the following equations. 4 x + 1 2 + 2 x + 3 2 4 x 2 + 12 x + 9 = 61 26

Given : 4 x + 1 2 + 2 x + 3 2 4 x 2 + 12 x + 9 = 61 26 We first put x = 0 in the expression and obtain: 4 0 + 1 2 + 2 0 + 3 2 4 0 2 + 12 0 + 9 = 61 26 ⇒ 10 9 = 61 26 which does not hold true. &there4; x=0 is not a solution. Consider the given equation: 4 x + 1 2 + 2 x + 3 2 4 x 2 + 12 x + 9 = 61 26 Apply dividendo: ⇒ 4 x + 1 2 2 x + 3 2 = 25 36 ⇒ 4 x + 1 2 x + 3 = ± 5 6 Case I: If : 4 x + 1 2 x + 3 = 5 6 Cross multiply and obtain: 24 x + 6 = 10 x + 15 ⇒ 14 x = 9 ⇒ x = 9 14 Case II: If: 4 x + 1 2 x + 3 = - 5 6 Cross multiply and obtain: 24 x + 6 = - 10 x - 15 ⇒ 34 x = - 21 ⇒ x = - 21 34 &there4; x = 9 14 , - 21 34 are the solutions.

E M B I B E

MHB - Math Part-I>Chapter 4 - Ratio and Proportion>Practice set

Maharashtra Board Solutions for Chapter: Ratio and Proportion, Exercise 3: Practice set

Author:Maharashtra Board

Maharashtra Board Mathematics Solutions for Exercise - Maharashtra Board Solutions for Chapter: Ratio and Proportion, Exercise 3: Practice set

Attempt the practice questions on Chapter 4: Ratio and Proportion, Exercise 3: Practice set with hints and solutions to strengthen your understanding. MHB - Math Part-I solutions are prepared by Experienced Embibe Experts.