1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Properties of Determinants
If a+b+c=-46 ...
Question
If a+b+c=-46 and the roots x,y,z of x^3+ax^2+bx+c are integers and greater than 2 then x-y+z is equal to
Open in App
Solution
Suggest Corrections
3
Similar questions
Q.
If
a
x
2
+
b
x
+
c
=
0
has imaginary roots and
a
−
b
+
c
>
0
,
then the set of points
(
x
,
y
)
satisfying the equation
∣
∣
a
(
x
2
+
y
z
)
+
(
b
+
1
)
x
+
c
∣
∣
=
|
a
x
2
+
b
x
+
c
|
+
|
x
+
y
|
consists of the region in the
x
y
−
plane which is
Q.
Consider equation
I
:
x
+
y
+
z
=
46
where
x
,
y
, and
z
are positive integers, and equation II:
x
+
y
+
z
+
w
=
46
, where
x
,
y
,
z
and
w
are positive integers. Then
Q.
(i) If a(y+z) = b(z+x) = c(x+y) and out of a, b, c no two of them are equal then
show that,
y
-
z
a
b
-
c
=
z
-
x
b
c
-
a
=
x
-
y
c
a
-
b
(ii) If
x
3
x
-
y
-
z
=
y
3
y
-
z
-
x
=
z
3
z
-
x
-
y
and
x
+
y
+
z
≠
0
then show that the value of each ratio is equal to 1.
(iii) If
a
x
+
b
y
x
+
y
=
b
x
+
a
z
x
+
z
=
a
y
+
b
z
y
+
z
and
x
+
y
+
z
≠
0
then show that
a
+
b
2
.
(iv) If
y
+
z
a
=
z
+
x
b
=
x
+
y
c
then show that
x
b
+
c
-
a
=
y
c
+
a
-
b
=
z
a
+
b
-
c
.
(v) If
3
x
-
5
y
5
z
+
3
y
=
x
+
5
z
y
-
5
x
=
y
-
z
x
-
z
then show that every ratio =
x
y
.
Q.
If
x
3
+
y
3
+
z
3
=
6
x
y
z
, where x, y, z are non-zero integers,
x
+
y
+
z
≠
0
and
x
y
z
=
x
+
y
+
z
, then the value of
(
x
–
y
)
2
+
(
y
–
z
)
2
+
(
z
–
x
)
2
is equal to
Q.
If
a
x
−
1
=
b
c
,
b
y
−
1
=
a
c
,
c
z
−
1
=
a
b
such that
x
,
y
,
z
are integers then value of
x
y
+
y
z
+
z
x
–
x
y
z
is
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
Properties
MATHEMATICS
Watch in App
Explore more
Properties of Determinants
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