factorise x^4/4 + 4/x^4+2
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Answer:
Given : x
4
+
x
4
4
We can further write it as
x
4
+
x
4
4
=x
4
+
x
4
4
+4−4
It can also written as
x
4
+
x
4
4
=(x
2
)
2
+(
x
2
2
)
2
+2×x
2
×(
x
2
2
)−2
2
.
x
4
+
x
4
4
=[(x
2
)
2
+(
x
2
2
)
2
+2×x
2
×(
x
2
2
)]−2
2
x
4
+
x
4
4
=(x
2
+
x
2
2
)
2
−2
2
On further simplification
Based on the equation a
2
−b
2
=(a+b)(a−b)
We get
x
4
+
x
4
4
=(x
2
+
x
2
2
+2)(x
2
+
x
2
2
−2).
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