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Byju's Answer
Standard X
Mathematics
Subtriplicate Ratio
Q 7 ans fast ...
Question
Q 7 ans fast
Q
7
.
I
f
x
+
y
a
x
+
b
y
=
y
+
z
a
y
+
b
z
=
z
+
x
a
z
+
b
x
,
p
r
o
v
e
t
h
a
t
e
a
c
h
r
a
t
i
o
i
s
e
q
u
a
l
t
o
2
a
+
b
,
u
n
l
e
s
s
x
+
y
+
z
=
0
.
Open in App
Solution
Hi,
We
know
from
componendo
-
divindo
that
If
a
b
=
c
d
=
e
f
then
it
is
also
equal
to
=
a
+
c
+
e
b
+
d
+
f
so
here
x
+
y
ax
+
by
=
y
+
z
ay
+
bz
=
z
+
x
az
+
bx
=
x
+
y
+
y
+
z
+
z
+
x
ax
+
by
+
ay
+
bz
+
az
+
bx
=
2
x
+
y
+
z
x
a
+
b
+
y
a
+
b
+
z
a
+
b
=
2
x
+
y
+
z
a
+
b
x
+
y
+
z
Now
if
x
+
y
+
z
is
non
zero
then
=
2
a
+
b
Hence
proved
Suggest Corrections
0
Similar questions
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
y
+
z
-
x
=
y
z
+
x
-
y
=
z
x
+
y
-
z
and x + y + z
≠
0 then show that each ratio is equal to 1.
Q.
If
x
x
+
2
y
+
z
=
y
y
+
2
z
+
x
=
z
z
+
2
x
+
y
and x + y + z
≠
0, then show that each ratio is equal to
1
4
.
Q.
If
a
x
+
b
y
+
c
z
=
1
,
b
x
+
c
y
+
a
z
=
0
=
c
x
+
a
y
+
b
z
, then
∣
∣ ∣
∣
x
y
z
z
x
y
y
z
x
∣
∣ ∣
∣
∣
∣ ∣
∣
a
b
c
c
a
b
b
c
a
∣
∣ ∣
∣
is equal to
Q.
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 each ratio is
a
+
b
2
.
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