MHR • Advanced Functions 12 Solutions 660

Chapter 7 Section 4 Question 16 Page 392
D;
"
#
$
10 ! v
1+ v
u + uv + v = 10
u(1+ v) = 10 ! v
%
&
'
2
u = 10 ! v
1+ v
+ v 2 = 40
" 100 ! 20v + v 2 %
$
# 1+ 2v + v 2 ' = 40 ! v2
&
100 ! 20v + v 2 = 40 ! v 2
v 4 + 2v 3 + v 2 ! 39v 2 ! 20v ! 80v +100 ! 40 = 0
( )( 1+ 2v + v )
2
100 ! 20v + v 2 = 40 + 80v + 40v 2 ! v 2 ! 2v 3 ! v 4
v 4 + 2v 3 ! 38v 2 !100v + 60 = 0
v &= 0.5 or v &= 6.3 since it is a positive real number.
Case 1: v &= 0.5
u =
10 ! (0.5)
1+ (0.5)
&= 6.3
Case 2: v &= 6.3
u =
10 ! (6.3)
1+ (6.3)
&= 0.5
u + v &= 6.3 + 0.5
&= 6.8
The closest integer value is 7.
MHR • Advanced Functions 12 Solutions 720