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Byju's Answer
Standard X
Mathematics
Quadratic Equations
aa x-1+bb x-1...
Question
a
(
a
x
-
1
)
+
b
(
b
x
-
1
)
=
(
a
+
b
)
,
x
≠
1
a
,
1
b
Open in App
Solution
a
(
a
x
−
1
)
+
b
(
b
x
−
1
)
=
(
a
+
b
)
⇒
[
a
(
a
x
−
1
)
−
b
]
+
[
b
(
b
x
−
1
)
−
a
]
=
0
⇒
a
−
b
(
a
x
−
1
)
a
x
−
1
+
b
−
a
(
b
x
−
1
)
b
x
−
1
=
0
⇒
a
−
a
b
x
+
b
a
x
−
1
+
a
−
a
b
x
+
b
b
x
−
1
=
0
⇒
(
a
−
a
b
x
+
b
)
[
1
(
a
x
−
1
)
+
1
(
b
x
−
1
)
]
=
0
⇒
(
a
−
a
b
x
+
b
)
[
(
b
x
−
1
)
+
(
a
x
−
1
)
(
a
x
−
1
)
(
b
x
−
1
)
]
=
0
⇒
(
a
−
a
b
x
+
b
)
[
(
a
+
b
)
x
−
2
(
a
x
−
1
)
(
b
x
−
1
)
]
=
0
⇒
(
a
−
a
b
x
+
b
)
[
(
a
+
b
)
x
−
2
]
=
0
⇒
a
−
a
b
x
+
b
=
0
or
(
a
+
b
)
x
−
2
=
0
⇒
x
=
(
a
+
b
)
a
b
or
x
=
2
(
a
+
b
)
Hence, the roots of the equation are
(
a
+
b
)
a
b
and
2
(
a
+
b
)
.
Suggest Corrections
0
Similar questions
Q.
Let a, b, c be such that b
(
a
+
c
)
≠
0
. If
∣
∣ ∣
∣
a
a
+
1
a
−
1
−
b
b
+
1
b
−
1
c
c
−
1
c
+
1
∣
∣ ∣
∣
+
∣
∣ ∣ ∣
∣
a
+
1
b
+
1
c
−
1
a
−
1
b
−
1
c
+
1
(
−
1
)
n
+
2
a
(
−
1
)
n
+
1
b
(
−
1
)
n
c
∣
∣ ∣ ∣
∣
=
0
Then the value of n is?
Q.
t
a
n
−
1
a
+
t
a
n
−
1
b
, where a>0,b>0,ab>1, is equal to
