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Standard IX
Mathematics
Question
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
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Solution
Verified by Toppr
y
+
z
a
=
z
+
x
b
=
x
+
y
c
=
K
(
y
+
z
)
=
a
k
,
(
z
+
x
)
=
b
k
,
(
x
+
y
)
=
c
k
b+c-a =
1
k
(
z
+
x
+
x
+
y
−
y
−
z
)
=
2
x
k
c
+
a
−
b
=
1
k
(
x
+
y
+
y
+
z
−
x
)
=
2
y
k
a
+
3
−
c
=
1
k
(
y
+
z
+
z
+
x
−
x
−
y
)
=
2
z
k
∴
x
b
+
c
−
a
=
x
2
x
/
k
=
k
/
2
y
c
+
a
−
b
=
k
/
2
=
z
a
+
b
−
c
=
x
b
+
c
−
a
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Similar Questions
Q1
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
View Solution
Q2
If
∣
∣ ∣
∣
a
b
−
y
c
−
z
a
−
x
b
c
−
z
a
−
x
b
−
y
c
∣
∣ ∣
∣
=
0
,
then
a
x
+
b
y
+
c
z
=
.
.
.
.
.
.
View Solution
Q3
If
x
b
+
c
-
a
=
y
c
+
a
-
b
=
z
a
+
b
-
c
.
then show that x(b
-
c) + y (c
-
a) + z (a
-
b) = 0.
View Solution
Q4
If
a
b
-
y
c
-
z
a
-
x
b
c
-
z
a
-
x
b
-
y
c
=
0, then using properties of determinants, find the value of
a
x
+
b
y
+
c
z
, where
x
,
y
,
z
≠
0.
View Solution
Q5
If
x
,
y
,
z
are different from zero and
Δ
=
∣
∣ ∣
∣
a
b
−
y
c
−
z
a
−
x
b
c
−
z
a
−
x
b
−
y
c
∣
∣ ∣
∣
=
0
, then the value of the expression
a
x
+
b
y
+
c
z
is ?
View Solution