Evaluate (x²-✓1-x²)⁴ + (x²+✓1-x²)⁴
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solve
(x
2
−
1−x
2
)
4
+(x
2
+
1−x
2
)
4
Medium
Solution
verified
Verified by Toppr
We know that a
2
+b
2
=(a+b)
2
−2ab
Take a=(x
2
−
1−x
2
)
2
and b=(x
2
+
1−x
2
)
2
Now (x
2
−
1−x
2
)
4
+(x
2
+
1−x
2
)
4
=((x
2
−
1−x
2
)
2
+(x
2
+
1−x
2
)
2
)−2((x
2
−
1−x
2
)
2
(x
2
+
1−x
2
)
2
)
=x
4
+1−x
2
−2x
1−x
2
+x
4
+1−x
2
+2x
1−x
2
−2((x
4
−1+x
2
)
2
)
=2x
4
+2−2x
2
−2((x
4
−1+x
2
)
2
)
=2x
4
+2−2x
2
−2(x
8
+1+x
4
−2x
4
−2x
2
+x
6
)
=2x
4
+2−2x
2
−2x
8
−2−2x
4
+4x
4
+4x
2
−2x
6
=−2x
8
−2x
6
+4x
4
+2x
2
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