Elementary Geometry for College Students (7th Edition)

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 5 - Section 5.4 - The Pythagorean Theorem - Exercises - Page 253: 35



Work Step by Step

We have to prove $c^{2} = a^{2} + b^{2}$ on putting given values $ a^{2} + b^{2 }= (p^{2}-q^{2})^{2} +(2pq)^{2}$ $= p^{4}+ q^{4}-2p^{2}q^{2}+4p^{2}p^{2}$ $= p^{4}+ q^{4}+2p^{2}q^{2}$ $=( p^{2}+q^{2})^{2}$ $= c^{2}$ hence proved
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