(X+3) (x+-3)=27 find the factorazations
Answers
Answered by
1
Step-by-step explanation:
Both
x
3
and
27
=
3
3
are perfect cubes. So we can use the difference of cubes identity:
a
3
−
b
3
=
(
a
−
b
)
(
a
2
+
a
b
+
b
2
)
with
a
=
x
and
b
=
3
as follows:
x
3
−
27
=
x
3
−
3
3
=
(
x
−
3
)
(
x
2
+
x
(
3
)
+
3
2
)
=
(
x
−
3
)
(
x
2
+
3
x
+
9
)
This is as far as you can go with Real coefficients. If you allow Complex coefficients then you can factor this a little further:
=
(
x
−
3
)
(
x
−
3
ω
)
(
x
−
3
ω
2
)
where
ω
=
−
1
2
+
√
3
2
i
is the primitive Complex cube root of
1
.
Answered by
1
Answer:
(X+3) (x-3)=27
x^2-3x+3x-9=27
x^2=27+9
x^2=36
X=6
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