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Byju's Answer
Standard X
Mathematics
Dividendo
Using the pro...
Question
Using the properties of proportion, solve the following equation for
x
.
x
3
+
3
x
3
x
2
+
1
=
341
91
11
Open in App
Solution
The correct option is
A
11
Given:
x
3
+
3
x
3
x
2
+
1
=
341
91
Applying componendo and dividendo, we get;
x
3
+
3
x
+
3
x
2
+
1
x
3
+
3
x
−
3
x
2
−
1
=
341
+
91
341
−
91
⇒
(
x
+
1
)
3
(
x
−
1
)
3
=
432
250
=
216
125
[
(
a
+
b
)
3
=
a
3
+
b
3
+
3
a
b
(
a
+
b
)
]
⇒
(
x
+
1
)
3
(
x
−
1
)
3
=
216
125
=
(
6
5
)
3
⇒
x
+
1
x
−
1
=
6
5
Again, appplying componendo and dividendo we get:
x
+
1
+
x
−
1
x
+
1
−
x
+
1
=
6
+
5
6
−
5
⇒
2
x
2
=
11
1
⇒
x
=
11
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0
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Q.
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