Paper 4: Fundamentals of Business Mathematics & Statistic

2.36 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Algebra

Example 48 : Simplify

a b 2 b c 2 c a 2

a b c 4

(x ) .(x ) .(x )

(x ,x ,x )

+ + +

Solution : =

a b 2 b c 2 c a 2

a b c 4

(x ) .(x ) .(x )

(x ,x ,x )

+ + +

2a 2b 2b 2c 2c 2a m n mn

a b c 4

x .x .x (since (a ) a )

(x ,x ,x )

+ + +

= =

2a 2b 2b 2c 2c 2a m n m n

a b c 4

x (a a a )

(x )

+ + + + + +

= + + × =

4 a 4b 4c

4a 4b 4c

x 1

x

+ +

= + + =

Example 49 : Find the value of

7 5^34732

8 35 5 3^183

x x x y

x y x− (x )

×

Solution : Now ( )

(^4) 7 5 (^3732)
(^835) 5 3 1/8^3
x x x y
x y x− x

= ×

(^4) 7 5 7 3 3
3 35 8
(^4) 7 5 73 3 2 2
3 5 38 5 5 3/8 3/8
x x x y x x y
x y x x x .y x

• 
  
  
  
  • = − × = −
    =[x^4 7 5 7 5 8 8+^3 +3 3 3 3− + − ][y ] xy.2 1− =
    Example 50 : If m a ,n a anda [m n ]= x = y^2 = y x z Prove that xyz = 1
    Solution :
    m a= x m a ,n ay xy y n ax xy
    [m n ] [a a ] ay x z = xy xyz = 2xyz=a (given) xyz 1^2
    Example 51 : If x y,y z,z xa= b= c= prove that abc = 1.
    Solution : We are given that
    x y,....(i) y z,....(ii) z x,....(iii)a= b= c=
    substituting the value of y from (i) in (ii)
    (x ) z i.e., x za b= ab= ....(iv)
    substituting the value of x from (iii) in (iv)
    (z ) z i.e. zc ab= abc=z
    Equating powers on the same base we get abc = 1
    abc = 1