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Byju's Answer
Standard VI
Mathematics
Solution of an Equation
Solve the fol...
Question
Solve the following equations
(i)
2
x
-
3
x
2
-
2
x
+
3
=
3
x
-
5
x
2
-
3
x
+
5
(ii)
3
x
2
+
21
x
+
4
3
x
2
+
27
x
+
5
=
x
+
7
x
+
9
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Solution
(
i
)
2
x
-
3
x
2
-
2
x
+
3
=
3
x
-
5
x
2
-
3
x
+
5
(
Given
)
⇒
x
2
-
2
x
+
3
2
x
-
3
=
x
2
-
3
x
+
5
3
x
-
5
Invertendo
⇒
x
2
-
2
x
+
3
+
2
x
-
3
2
x
-
3
=
x
2
-
3
x
+
5
+
3
x
-
5
3
x
-
5
Componendo
⇒
x
2
2
x
-
3
=
x
2
3
x
-
5
Now
,
for
x
=
0
,
the
equation
is
evidently
satisfied
.
Therefore
,
x
=
0
is
one
of
the
solutions
.
O
r
,
1
2
x
-
3
=
1
3
x
-
5
Dividing
by
x
2
⇒
3
x
-
5
=
2
x
-
3
⇒
x
=
2
Hence
,
x
=
0
or
x
=
2
is
the
solution
.
(
ii
)
3
x
2
+
21
x
+
4
3
x
2
+
27
x
+
5
=
x
+
7
x
+
9
⇒
3
x
2
+
21
x
+
4
-
3
x
2
+
27
x
+
5
3
x
2
+
27
x
+
5
=
x
+
7
-
x
+
9
x
+
9
Dividendo
⇒
-
6
x
-
1
3
x
2
+
27
x
+
5
=
-
2
x
+
9
By
cross
-
multiplying
,
we
get
:
⇒
-
6
x
-
1
x
+
9
=
-
2
3
x
2
+
27
x
+
5
⇒
-
6
x
2
-
54
x
-
x
-
9
=
-
6
x
2
-
54
x
-
10
⇒
-
6
x
2
-
54
x
-
x
-
9
+
6
x
2
+
54
x
+
10
=
0
⇒
-
x
+
1
=
0
⇒
x
=
1
Hence
,
x
=
1
is
the
solution
.
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0
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Q.
Which of the following are quadratic equations?
(i) x
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+ 6x − 4 = 0
(ii)
3
x
2
-
2
x
+
1
2
=
0
(iii)
x
2
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2
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(iv)
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x
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(v)
2
x
2
-
3
x
+
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-
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x
-
x
-
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=
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2
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2
=
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x
+
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x
+
4
(xi) (2x + 1) (3x + 2) = 6(x − 1) (x − 2)
(xii)
x
+
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x
=
x
2
,
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≠
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(xiii) 16x
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(xv) x(x + 1) + 8 = (x + 2) (x − 2)
