Factorise :- x¹² = 1.
Answers
Answer:
x=1
Step-by-step explanation:
(1)12=1 by this we can get 1
Answer:
Factoring
x
12
−
1
can be tricky but can be broken down and worked it out step by step.
Let us recollect some rules.
Difference of squares
a
2
−
b
2
=
(
a
−
b
)
(
a
+
b
)
Difference of cubes
a
3
−
b
3
=
(
a
−
b
)
(
a
2
+
a
b
+
b
2
)
Sum of cubes
a
3
+
b
3
=
(
a
+
b
)
(
a
2
−
a
b
+
b
2
)
Now let us come to our problem.
x
12
−
1
Let us make x^12 into something which we can recognize easily.
x
12
=
x
6
⋅
2
=
(
x
6
)
2
We have used
a
m
n
=
(
a
m
)
n
(
x
6
)
2
−
1
2
Now it is of form
a
2
−
b
2
(
x
6
−
1
)
(
x
6
+
1
)
Let us factorize
x
6
−
1
x
6
−
1
=
(
x
3
)
2
−
1
2
Rewriting
x
6
to get into
a
2
−
b
2
form
x
6
−
1
=
(
x
3
−
1
)
(
x
3
+
1
)
x
6
−
1
=
(
x
−
1
)
(
x
2
+
x
+
1
)
(
x
+
1
)
(
x
2
−
x
+
1
)
Now to factorize
(
x
6
+
1
)
x
6
+
1
=
(
x
2
)
3
+
1
3
Rewriting
x
6
to get it into
a
3
+
b
3
form
x
6
+
1
=
(
x
2
+
1
)
(
x
4
−
x
2
+
1
)
Factors of
(
x
6
−
1
)
(
x
6
+
1
)
=
(
x
−
1
)
(
x
2
+
x
+
1
)
(
x
+
1
)
(
x
2
−
x
+
1
)
(
x
2
+
1
)
(
x
4
−
x
2
+
1
)
Rearranging
(
x
−
1
)
(
x
+
1
)
(
x
2
+
1
)
(
x
2
−
x
+
1
)
(
x
2
+
x
+
1
)
(
x
4
−
x
2
+
1
)
Answer