BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.7, Problem 104E
To determine

To show:that ab<a+cb+d<cd where a,b,c,and d are positive numbers.

Expert Solution

Explanation of Solution

Given:

The given condition is a,b,c,and d are positive numbers such that ab<cd .

Calculation:

According to the question, the given inequality is

  ab<cd .

The inequality is expressed as

  ab<cdad<bc{crossmultiplication}ad+ab<bc+ab{addabonboththesides}a(d+b)<b(c+a)ab<a+cb+d.........(1)

Also, the expression is expressed as

  ab<cdad<bc{crossmultiplication}ad+cd<bc+cd{addcdonboththesides}d(a+c)<c(b+d)a+cb+d<cd.........(2)

From (1) and (2), it is found that

  ab<a+cb+d<cd

Hence, the equation is proved.

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