the value of a-2b=15 and ab=11 what is the value of a^2+4b^2
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1
Answer:
Method I
Given that,
a
−
2
b
=
15
∴
(
a
−
2
b
)
2
=
15
2
=
225
.
∴
a
2
−
2
⋅
a
⋅
2
b
+
4
b
2
=
225
,
i.e.,
a
2
−
4
a
b
+
4
b
2
=
225
.
Letting,
a
b
=
11
in this, we have,
a
2
−
4
(
11
)
+
4
b
2
=
225
.
Hence,
a
2
+
4
b
2
=
225
+
44
=
269
.
Method II
Notice that
(
a
+
2
b
)
2
+
(
a
−
2
b
)
2
=
2
(
a
2
+
4
b
2
)
.
Here, we replace
(
a
+
2
b
)
2
by
(
a
−
2
b
)
2
+
8
a
b
,
to get,
(
a
−
2
b
)
2
+
8
a
b
+
(
a
−
2
b
)
2
=
2
(
a
2
+
4
b
2
)
,
.
& now putting the given values,
225
+
8
⋅
11
+
225
=
2
(
a
2
+
4
b
2
)
=
538
,
so,
(
a
2
+
4
b
2
)
=
538
2
=
269
,
as before!
Step-by-step explanation:
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