Algebra 1
Algebra 1
1st Edition
ISBN: 9780078884801
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 10.3, Problem 36HP
To determine

To determine if the statement is true or false and provide an example.

Expert Solution & Answer
Check Mark

Answer to Problem 36HP

True

Explanation of Solution

Given:

Statement: x+y>x2+y2 when x>0 and y>0

Consider the expression in the given statement.

  x+y>x2+y2

In both the left-hand and right-hand sides, the variables are positive. Hence, each side of the given in equality represents a positive number.

That is,

  x+y>x2+y2

Squaring on both the sides,

   (x+y) 2 > ( x 2 + y 2 ) 2 (x+y) 2 > x 2 + y 2

Expanding the left-hand side,

  x2+2xy+y2>x2+y2

Both the sides x2 and y2 gets cancelled giving,

  2xy>0

Therefore, the left-hand side is obviously greater than the right-hand side.

Conclusion:

Therefore, x+y>x2+y2 is true when x>0 and y>0 .

Chapter 10 Solutions

Algebra 1

Ch. 10.1 - Prob. 2CYUCh. 10.1 - Prob. 3CYUCh. 10.1 - Prob. 4CYUCh. 10.1 - Prob. 5CYUCh. 10.1 - Prob. 6CYUCh. 10.1 - Prob. 7CYUCh. 10.1 - Prob. 8CYUCh. 10.1 - Prob. 9CYUCh. 10.1 - Prob. 10CYUCh. 10.1 - Prob. 11CYUCh. 10.1 - Prob. 12CYUCh. 10.1 - Prob. 13CYUCh. 10.1 - Prob. 14PPSCh. 10.1 - Prob. 15PPSCh. 10.1 - Prob. 16PPSCh. 10.1 - Prob. 17PPSCh. 10.1 - Prob. 18PPSCh. 10.1 - Prob. 19PPSCh. 10.1 - Prob. 20PPSCh. 10.1 - Prob. 21PPSCh. 10.1 - Prob. 22PPSCh. 10.1 - Prob. 23PPSCh. 10.1 - Prob. 24PPSCh. 10.1 - Prob. 25PPSCh. 10.1 - Prob. 26PPSCh. 10.1 - Prob. 27PPSCh. 10.1 - Prob. 28PPSCh. 10.1 - Prob. 29PPSCh. 10.1 - Prob. 30PPSCh. 10.1 - Prob. 31PPSCh. 10.1 - Prob. 32PPSCh. 10.1 - Prob. 33PPSCh. 10.1 - Prob. 34PPSCh. 10.1 - Prob. 35PPSCh. 10.1 - Prob. 36PPSCh. 10.1 - Prob. 37PPSCh. 10.1 - Prob. 38PPSCh. 10.1 - Prob. 39PPSCh. 10.1 - Prob. 40PPSCh. 10.1 - Prob. 41PPSCh. 10.1 - Prob. 42PPSCh. 10.1 - Prob. 43PPSCh. 10.1 - Prob. 44PPSCh. 10.1 - Prob. 45HPCh. 10.1 - Prob. 46HPCh. 10.1 - Prob. 47HPCh. 10.1 - 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Prob. 47PPSCh. 10.8 - Prob. 48PPSCh. 10.8 - Prob. 49PPSCh. 10.8 - Prob. 50PPSCh. 10.8 - Prob. 51HPCh. 10.8 - Prob. 52HPCh. 10.8 - Prob. 53HPCh. 10.8 - Prob. 54HPCh. 10.8 - Prob. 56STPCh. 10.8 - Prob. 58STPCh. 10.8 - Prob. 60SRCh. 10.8 - Prob. 61SRCh. 10.8 - Prob. 62SRCh. 10.8 - Prob. 63SRCh. 10.8 - Prob. 64SRCh. 10.8 - Prob. 65SRCh. 10.8 - Prob. 66SRCh. 10.8 - Prob. 68SCh. 10.8 - Prob. 69SCh. 10.8 - Prob. 70SCh. 10.8 - Prob. 71SCh. 10.8 - Prob. 1CYPCh. 10.8 - Prob. 55HPCh. 10.8 - Prob. 57STPCh. 10.8 - Prob. 59STPCh. 10.8 - Prob. 67SRCh. 10 - Prob. 11QCCh. 10 - Prob. 12QCCh. 10 - Prob. 13QCCh. 10 - Prob. 14QCCh. 10 - Prob. 15QCCh. 10 - Prob. 16QCCh. 10 - Prob. 17QCCh. 10 - Prob. 18QCCh. 10 - Prob. 1QCCh. 10 - Prob. 2QCCh. 10 - Prob. 3QCCh. 10 - Prob. 4QCCh. 10 - Prob. 5QCCh. 10 - Prob. 6QCCh. 10 - Prob. 7QCCh. 10 - Prob. 8QCCh. 10 - Prob. 9QCCh. 10 - Prob. 10QCCh. 10 - Prob. 1MCQCh. 10 - Prob. 2MCQCh. 10 - Prob. 3MCQCh. 10 - Prob. 4MCQCh. 10 - Prob. 5MCQCh. 10 - Prob. 6MCQCh. 10 - Prob. 7MCQCh. 10 - Prob. 8MCQCh. 10 - Prob. 9MCQCh. 10 - Prob. 10MCQCh. 10 - Prob. 11MCQCh. 10 - Prob. 12MCQCh. 10 - Prob. 14MCQCh. 10 - Prob. 15MCQCh. 10 - Prob. 16MCQCh. 10 - Prob. 17MCQCh. 10 - Prob. 18MCQCh. 10 - Prob. 19MCQCh. 10 - Prob. 20MCQCh. 10 - Prob. 21MCQCh. 10 - Prob. 22MCQCh. 10 - Prob. 23MCQCh. 10 - Prob. 24MCQCh. 10 - Prob. 25MCQCh. 10 - Prob. 26MCQCh. 10 - Prob. 27MCQCh. 10 - Prob. 28MCQCh. 10 - Prob. 29MCQCh. 10 - Prob. 1SGRCh. 10 - Prob. 2SGRCh. 10 - Prob. 3SGRCh. 10 - Prob. 4SGRCh. 10 - Prob. 5SGRCh. 10 - Prob. 6SGRCh. 10 - Prob. 7SGRCh. 10 - Prob. 8SGRCh. 10 - Prob. 9SGRCh. 10 - Prob. 10SGRCh. 10 - Prob. 11SGRCh. 10 - Prob. 12SGRCh. 10 - Prob. 13SGRCh. 10 - Prob. 14SGRCh. 10 - Prob. 15SGRCh. 10 - Prob. 16SGRCh. 10 - Prob. 17SGRCh. 10 - Prob. 18SGRCh. 10 - Prob. 19SGRCh. 10 - Prob. 20SGRCh. 10 - Prob. 21SGRCh. 10 - Prob. 22SGRCh. 10 - Prob. 23SGRCh. 10 - Prob. 24SGRCh. 10 - Prob. 25SGRCh. 10 - Prob. 26SGRCh. 10 - Prob. 27SGRCh. 10 - Prob. 28SGRCh. 10 - Prob. 29SGRCh. 10 - Prob. 30SGRCh. 10 - Prob. 31SGRCh. 10 - Prob. 32SGRCh. 10 - Prob. 33SGRCh. 10 - Prob. 34SGRCh. 10 - Prob. 35SGRCh. 10 - Prob. 36SGRCh. 10 - Prob. 37SGRCh. 10 - Prob. 38SGRCh. 10 - Prob. 39SGRCh. 10 - Prob. 40SGRCh. 10 - Prob. 41SGRCh. 10 - Prob. 42SGRCh. 10 - Prob. 43SGRCh. 10 - Prob. 44SGRCh. 10 - Prob. 45SGRCh. 10 - Prob. 46SGRCh. 10 - Prob. 47SGRCh. 10 - Prob. 48SGRCh. 10 - Prob. 49SGRCh. 10 - Prob. 50SGRCh. 10 - Prob. 51SGRCh. 10 - Prob. 52SGRCh. 10 - Prob. 53SGRCh. 10 - Prob. 54SGRCh. 10 - Prob. 55SGRCh. 10 - Prob. 56SGRCh. 10 - Prob. 57SGRCh. 10 - Prob. 58SGRCh. 10 - Prob. 59SGRCh. 10 - Prob. 60SGRCh. 10 - Prob. 61SGRCh. 10 - Prob. 62SGRCh. 10 - Prob. 63SGRCh. 10 - Prob. 64SGRCh. 10 - Prob. 65SGRCh. 10 - Prob. 66SGRCh. 10 - Prob. 67SGRCh. 10 - Prob. 1PTCh. 10 - Prob. 2PTCh. 10 - Prob. 3PTCh. 10 - Prob. 4PTCh. 10 - Prob. 5PTCh. 10 - Prob. 6PTCh. 10 - Prob. 7PTCh. 10 - Prob. 8PTCh. 10 - Prob. 9PTCh. 10 - Prob. 10PTCh. 10 - Prob. 11PTCh. 10 - Prob. 12PTCh. 10 - Prob. 13PTCh. 10 - Prob. 14PTCh. 10 - Prob. 15PTCh. 10 - Prob. 16PTCh. 10 - Prob. 17PTCh. 10 - Prob. 18PTCh. 10 - Prob. 19PTCh. 10 - Prob. 20PTCh. 10 - Prob. 21PTCh. 10 - Prob. 22PTCh. 10 - Prob. 23PTCh. 10 - Prob. 25PTCh. 10 - Prob. 27PTCh. 10 - Prob. 1STPCh. 10 - Prob. 2STPCh. 10 - Prob. 3STPCh. 10 - Prob. 4STPCh. 10 - Prob. 5STPCh. 10 - Prob. 6STPCh. 10 - Prob. 7STPCh. 10 - Prob. 8STPCh. 10 - Prob. 9STPCh. 10 - Prob. 11STPCh. 10 - Prob. 12STPCh. 10 - Prob. 13STPCh. 10 - Prob. 14STPCh. 10 - Prob. 15STPCh. 10 - Prob. 13MCQCh. 10 - Prob. 24PTCh. 10 - Prob. 26PTCh. 10 - Prob. 10STPCh. 10 - Prob. 16STP
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