Geometry: An Interactive Journey to Mastery

Solutions

,IZHEHOLHYHWKDWWKHJHRPHWULFIRUPXODZRUNVIRUIUDFWLRQVDVZHOODVZKROHQXPEHUVͼ௘UHDGRQ௘ͽWKHQ

23

44 499 9 1 1 1 9 9923

4 44

91

4 1

944

(^45) ,

 §· §· ̈ ̧ ̈ ̧©¹ ©¹

(^) 
(^) 

""^

JLYLQJWKHWRWDODUHDRIWKHVQRZÀDNHWREH1.˜ 114 8335 5

7KHTXHVWLRQWKDWUHPDLQVLVDVIROORZV6KRXOGxx x11 1 23 "equalx^1  1 , even if x is not

DZKROHQXPEHU"

Notice that 11 1xx x   23 ""1111 1xxxx x§· ̈ ̧©¹ 23.

If xx x11 1 23 " equals A, then this equation reads AA ˜^11 xx.

0XOWLSO\LQJWKURXJKE\x and solving for A gives

1

11

(^11).
xA A
xA
A x





(^) 
6RLWVHHPVWKDWZHGRLQGHHGKDYH11 1xx x 23 " x^1  1.
&KDOOHQJH'HYLVHDSDSHUWHDULQJH[HUFLVHWKDWVKRZVWKDW
23

11 1 91.

94  9944 " 4  1

5. 7KHWH[WXUHGVXUIDFHKDVWKHJUHDWHVWVXUIDFHDUHDDQGWKHUHIRUHUHTXLUHVPRUHSDLQWWRFRYHU