Geometry: An Interactive Journey to Mastery

Solutions

This gives

x^2222222   222,cxc y k x cxc y k xc y 2 2

yielding

24 kxc y k cx  ^222

or

xc y ^222 kcx^2 k.

6TXDULQJDJDLQJLYHV

xc y ^22 kcx 4222 2,cx^4 k 2

DQGH[SDQGLQJJLYHV

xcxcy^222  22,kcx 4222 cx^4 k 2

yielding

xyc^222 ©¹ ̈ ̧§·1. ^4 kck 2224

Because k! 2 c, the quantities 1and^4 kck 2224 c^2 DUHERWKSRVLWLYHQXPEHUV'LYLGLQJWKURXJKE\k 42 c^2

gives

(^222222)
22

1,

44 4

1

x y

k c k c

kc

§·§·  

̈ ̧ ̈ ̧ ̈ ̧©¹

̈ ̧©¹

which is indeed an equation of the form abx^222  y^21 ͼ௘ZLWK

(^222)
2 2
2
(^44) and 4.
1
k c k
abcc
k

 · ̧

 ¹^