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Byju's Answer
Standard IX
Mathematics
Exponential Representation for Irrational Numbers
Find those va...
Question
Find those values of c for which the equations
2
x
+
3
y
=
3
(
c
+
2
)
x
+
(
c
+
4
)
y
=
(
c
+
6
)
(
c
+
2
)
2
x
+
(
c
+
4
)
2
y
=
(
c
+
6
)
2
are consistent.
Find the sum of squares of all the values of c?
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Solution
Given system of equations is consistent
D
=
0
⇒
∣
∣ ∣ ∣
∣
2
3
3
c
+
2
c
+
4
c
+
6
(
c
+
2
)
2
(
c
+
4
)
2
(
c
+
6
)
2
∣
∣ ∣ ∣
∣
=
0
C
1
→
C
1
−
C
3
;
C
2
→
C
2
−
C
3
∣
∣ ∣ ∣
∣
−
1
0
3
−
4
−
2
c
+
6
−
4
(
2
c
+
8
)
−
2
(
2
c
+
10
)
(
c
+
6
)
2
∣
∣ ∣ ∣
∣
=
0
⇒
∣
∣ ∣ ∣
∣
1
0
3
4
1
c
+
6
8
c
+
32
2
c
+
10
(
c
+
6
)
2
∣
∣ ∣ ∣
∣
=
0
C
1
→
C
1
−
4
C
2
⇒
∣
∣ ∣ ∣
∣
1
0
3
0
1
c
+
6
−
8
2
c
+
10
(
c
+
6
)
2
∣
∣ ∣ ∣
∣
=
0
C
3
→
C
3
−
3
C
1
⇒
∣
∣ ∣ ∣
∣
1
0
0
0
1
c
+
6
−
8
2
c
+
10
(
c
+
6
)
2
+
24
∣
∣ ∣ ∣
∣
=
0
⇒
−
c
2
−
10
c
=
0
⇒
c
=
0
,
c
=
−
10
Sum of squares of c is
0
+
100
=
100
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0
Similar questions
Q.
The sum of square of values of
c
for which the equations
2
x
+
3
y
=
3
(
c
+
2
)
x
+
(
c
+
4
)
y
=
(
c
+
6
)
(
c
+
2
)
2
x
+
(
c
+
4
)
2
y
=
(
c
+
6
)
2
are consistent, is
Q.
Find those values of c for which the equations:
2
x
+
3
y
=
3
(
c
+
2
)
x
+
(
c
+
4
)
y
=
c
+
6
(
c
+
2
)
2
x
+
(
c
+
4
)
2
y
=
(
c
+
6
)
2
are consistent. Also solve above equations for these values of c.
Q.
A value of
c
for which the system of equations
x
+
y
=
1
(
c
+
2
)
x
+
(
c
+
4
)
y
=
6
(
c
+
2
)
2
x
+
(
c
+
4
)
2
y
=
36
is solvable (consistent) is
Q.
If the system of equations
x
+
y
=
1
,
(
c
+
2
)
x
+
(
c
+
4
)
y
=
6
,
(
c
+
2
)
2
x
+
(
c
+
4
)
2
y
=
36
are consistent, then the value of
c
can be
Q.
If the equations
x
+
y
=
1
,
(
c
+
2
)
x
+
(
c
+
4
)
y
=
6
,
(
c
+
2
)
2
x
+
(
c
+
4
)
2
y
=
36
are consistent, then
c
=
?
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