# To show that if 0 &lt; a &lt; b , then a 2 &lt; b 2

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter A, Problem 44E
To determine

## To calculate: To show that if 0<a<b , then a2<b2

Expert Solution

Its proved that if 0<a<b , then a2<b2

### Explanation of Solution

Given information: 0<a<b

Formula Used:

If a and b are real numbers, where c is non-zero real number, then the inequality a<b is same as

a+c<b+c

ac<bc   if c>0

ac>bc   if c<0

Calculation:

Given the following:

0<a<b

On simplifying,

a<bab<0

Since a>0,b>0 , thus a+b>0

Multiplying both sides of equation by (a+b) :

(ab)(a+b)<0(a+b)(ab)(a+b)<0a2b2<0a2<b2

Conclusion:

Hence, proved that a2<b2

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