Evaluate: (x2-1-x2)4+(x2+1-x2)4 - Mathematics

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Sum

Evaluate: `(x^2 - sqrt(1 - x^2))^4 + (x^2 + sqrt(1 - x^2))^4`

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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

Concept: Binomial Theorem for Positive Integral Indices
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Chapter 8: Binomial Theorem - Solved Examples [Page 132]

APPEARS IN

NCERT Mathematics Exemplar Class 11
Chapter 8 Binomial Theorem
Solved Examples | Q 4 | Page 132
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