1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Definition of Functions
Let a,b and...
Question
Let
a
,
b
and
c
be the sides of a
△
A
B
C
. If
a
2
,
b
2
,
c
2
are the roots of the equation
x
3
−
P
x
2
+
Q
x
−
R
=
0
, where
P
,
Q
,
R
are constants, then find the value of
cos
A
A
+
cos
B
B
+
cos
C
C
in terms of
P
,
Q
and
R
.
Open in App
Solution
Given,
cos
A
a
+
cos
B
b
+
cos
C
c
---------------------------(1)
Applying cosine rule:
cos
A
=
b
2
+
c
2
−
a
2
2
b
c
,
cos
B
=
a
2
+
c
2
−
b
2
2
a
c
,
cos
C
=
a
2
+
b
2
−
c
2
2
a
b
putting values in equation (1)
=
b
2
+
c
2
−
a
2
2
a
b
c
+
a
2
+
c
2
−
b
2
2
a
b
c
+
a
2
+
b
2
−
c
2
2
a
b
c
=
(
a
2
+
b
2
+
c
2
)
2
a
b
c
Now,
X
3
−
P
x
2
+
Q
x
−
R
=
0
Sum of roots,
a
2
+
b
2
+
c
2
=
P
Product of roots,
a
2
b
2
c
2
=
R
Then,
(
a
2
+
b
2
+
c
2
)
2
a
b
c
=
p
2
√
R
∴
cos
A
a
+
cos
B
b
+
cos
C
c
=
P
2
√
R
Suggest Corrections
0
Similar questions
Q.
Let
a
,
b
and
c
be the sides of a
Δ
A
B
C
. If
a
2
,
b
2
a
n
d
c
2
are the roots of the equation
(
x
3
−
P
x
2
+
Q
x
−
R
=
0
)
, where P, Q and R are constants then the value of
(
c
o
s
A
a
+
c
o
s
B
b
+
c
o
s
C
c
)
is equal to
Q.
Let P, Q , R be defined as
P
=
a
2
+
a
b
2
−
a
2
c
−
a
c
2
Q
=
b
2
+
b
c
2
−
a
2
b
−
a
b
2
R
=
a
2
c
+
c
2
a
−
c
2
b
−
c
b
2
where a, b, c are all +ive and the equation
P
x
2
+
Q
x
+
R
=
0
has equal roots then a , b , c are in
Q.
If
a
,
b
,
c
are the roots of the equation
x
3
−
p
x
2
+
q
x
−
r
=
0
find the value of
1
a
2
+
1
b
2
+
1
c
2
.
Q.
If
a
,
b
,
c
are the sides of the
Δ
A
B
C
and
a
2
,
b
2
,
c
2
are the roots of
x
3
−
p
x
2
+
q
x
−
k
=
0
,
then
Q.
Let equation
x
3
+
p
x
2
+
q
x
−
q
=
0
where
p
,
q
,
∈
R
−
{
0
}
has 3 real roots
α
,
β
,
λ
in
H
.
P
.
, then
Minimum value of
1
α
2
+
1
β
2
+
1
γ
2
is
(
You may use the inequality
a
2
+
b
2
+
c
2
≥
a
b
+
b
c
+
c
a
for any
a
,
b
,
c
∈
R
)
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Definition of Function
MATHEMATICS
Watch in App
Explore more
Definition of Functions
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app