Answer:
b = 40 and -40
General form of Perfect square trinomial is
a
2
+
2
a
b
+
b
2
Therefore from
16
x
2
−
b
x
+
25
a
2
=
√
16
x
2
,
b
2
=
25
, then
a
=
±
4
x
,
b
=
±
5
take consideration a=4x and b=-5 (different sign), then
−
b
x
=
2
(
4
x
)
(
−
5
)
−
b
x
=
−
40
x
b
=
40
The perfect square is
(
4
x
−
5
)
2
=
16
x
2
−
40
x
+
25
.
if we consider a=4x and b=5 (same sign), then
−
b
x
=
2
(
4
x
)
(
5
)
−
b
x
=
40
x
b
=
−
40
The perfect square is
(
4
x
+
5
)
2
=
16
x
2
+
40
x
+
25
.
The first solution
(
4
x
−
5
)
2
is the best solution after comparing the expression given.
