If (x+z) directly varies y and (y+z) directly varies x , then prove that (x+y) directly varies z.
Answers
Answered by
1
Step-by-step explanation:
Given
x
+
y
∝
z
⇒
x
+
y
=
m
z
...
...
.
[
1
]
, where m = proportionality constant
⇒
x
+
y
z
=
m
⇒
x
+
y
+
z
z
=
m
+
1
...
.
[
2
]
Again
y
+
z
∝
x
⇒
y
+
z
=
n
x
...
...
.
.
[
3
]
, where n = proportionality constant
⇒
y
+
z
x
=
n
⇒
x
+
y
+
z
x
=
n
+
1
...
...
[
4
]
Dividing [2] by [4]
x
z
=
m
+
1
n
+
1
=
k
(
s
a
y
)
⇒
x
=
k
z
...
...
[
5
]
By [1] and [5] we get
k
z
+
y
=
m
z
⇒
y
=
(
m
−
k
)
z
⇒
y
z
=
(
m
−
k
)
...
...
[
6
]
Dividing [2] by [6] we get
x
+
y
+
z
y
=
m
+
1
m
−
k
=
c
another constant
⇒
x
+
y
+
z
y
−
1
=
c
−
1
⇒
x
+
z
y
=
c
−
1
=
constant
Hence
z
+
x
∝
y
Proved
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