✔ 最佳答案
2. p, q, r are the lengths of the sides of ΔPQR in which∠PRQ=θ. The length r is 8 less that the product of the lengths p and q.
The lengths pa nd q are the roots of the quadratic equation x^2 - 8x +m = 0 where m≠0.
(i) Show that cosθ = (14=m)/2
(ii) Hence show that ΔPQR exist for 12<16.
(iii) And Hence, find the values of m for which θ is obtuse.
(i)
p+q=8
pqm
cosθ
=(p^2+q^2-(8-pq)^2)/2pq
=[(p+q)^2-2pq-64+16pq-p^2q^2]/2pq
=(64+14m-64-m^2)/2m
= (14-m)/2
(b)
Area of ΔPQR
=(1/2)pqsinθ
=(1/2)m√(1- [(14-m)/2]^2)
=(1/2)m√[(4-196+28m-m^2/4]
=(1/2)m√[-(m^2-28m+192)/4]
So m^2-28m+192<0
and then 12<m<16
(iii)
θ is obtuse implies cosθ<0
(14-m)/2<0
m>14
Combine with (ii)
The values of m is 14<m<16
2008-02-03 13:49:44 補充：
p and q are the roots of the quadratic equation x^2 - 8x +m = 0用SUM AND PRODUCT OF THE ROOTS
