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Question
Evaluate: `(x^2 - sqrt(1 - x^2))^4 + (x^2 + sqrt(1 - x^2))^4`
Solution
Putting `sqrt(1 - x^2)` = y, we get
The given expression = (x2 – y)4 + (x2 + y)4
= 2[x8 + 4C2 x4 y2 + 4C4 y4]
= `2 x^8 + (4 xx 3)/(2 xx 1) x^4 * (1 - x^2) + (1 - x^2)^2`
= 2[x8 + 6x4 (1 – x2) + (1 – 2x2 + x 4 ]
= 2x8 – 12x6 + 14x4 – 4x2 + 2
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