What should be
added to (x-4) (x+6) to get x^2-11x+24
Answers
Answered by
1
Step-by-step explanation:
The given eqn. is,
(
x
2
+
14
x
+
24
)
(
x
2
+
11
x
+
24
)
=
4
x
2
.
Let,
x
2
+
24
=
y
.
Then,
(
y
+
14
x
)
(
y
+
11
x
)
=
4
x
2
.
∴
y
2
+
(
14
x
+
11
x
)
y
+
(
14
x
)
(
15
x
)
−
4
x
2
=
0
,
i
.
e
.
,
y
2
+
25
x
y
+
154
x
2
−
4
x
2
=
0
,
or
,
y
2
+
25
x
y
+
150
x
2
=
0
.
∴
y
2
+
15
x
y
−−−−−−−−−
+
10
x
y
+
150
x
2
−−−−−−−−−−−−
=
0
.
∴
y
(
y
+
15
x
)
+
10
x
(
y
+
15
x
)
.
∴
(
y
+
15
x
)
(
y
+
10
x
)
=
0
.
Since,
y
=
x
2
+
24
,
we have,
∴
(
x
2
+
15
x
+
24
)
(
x
2
+
10
x
+
24
)
=
0
.
If,
x
2
+
15
x
+
24
=
0
,
then, using the quadratic formula,
x
=
−
15
±
√
15
2
−
4
⋅
1
⋅
24
2
⋅
1
=
−
15
±
√
225
−
96
2
.
∴
x
=
−
15
±
√
129
2
≈
−
15
±
11.36
2
,
or
,
x
≈
−
1.82
,
or
,
x
≈
−
13.18
.
If,
x
2
+
10
x
+
24
=
0
,
then,
(
x
+
6
)
(
x
+
4
)
=
0
.
∴
x
=
−
6
,
or
,
x
=
−
4
.
Hence, the Solution Set is
{
−
1.82
,
−
13.18
,
−
6
,
−
4
}
.
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