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Find the value of (sqrt(2)+1)^4-(sqrt(2)...

Find the value of `(sqrt(2)+1)^4-(sqrt(2)-1)^4dot`

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Verified by Experts

The correct Answer is:
`140sqrt(2)`
`(x+a)^(n)-(x-a)^(n) = 2[.^(n)C_(1)x^(n-1)a+.^(n)C_(3)x^(n-3)a^(3)+.^(n)C_(5)x^(n-5)a^(5)+"……"]`
`:. (sqrt(2)+1)^(6)-(sqrt(2)-1)^(6)`
`= 2[.^(6)C_(1)(sqrt(2))^(5)(1)^(1)+.^(6)C_(3)(sqrt(2))^(3)+.^(6)C_(5)(sqrt(2))^(1)(1)^(5)]`
`= 2[6 xx 4 sqrt(2) + 20 xx 2 sqrt(2) + 6 sqrt(2)]`
`= 2[24sqrt(2)+40sqrt(2)+6sqrt(2)] = 140sqrt(2)`
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CENGAGE PUBLICATION-BINOMIAL THEOREM-Concept Application Exercise 8.1
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  2. about to only mathematics

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  3. The two successive terms in the expansion of (1+x)^24 whose coefficie...

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  4. If the number of terms in the expansion of (x+y+z)^n are 36, then find...

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  5. Find the value of 1/(81^n)-((10)/(81^n))^(2n)C1+((10^2)/(81^n))^(2n)C2...

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  6. prove that sum(r=0)^n(-1)^r^n Cr. [1/(2^r)+(3^r)/(2^(2r))+(7^r)/(2^(...

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  7. In (3 3+1/(3 3))^n if the ratio of 7th term from the beginning to the ...

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  8. If the coefficients of (r-5) th and(2r-1) th terms in the expansion of...

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  9. Find the number of irrational terms in the expansion of (5^(1//6)+2^(1...

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  10. Represent cos 6 theta in terms of cos theta.

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  11. Find the number of nonzero terms in the expansion of (1+3sqrt(2)x)^9+(...

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  12. Find the value of (sqrt(2)+1)^4-(sqrt(2)-1)^4dot

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  13. Find the degree of the polynomial 1/(sqrt(4x+1)){((1+sqrt(4x+1))/2)^7-...

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  14. Let R=(5 sqrt 5+11)^(2n+1) and f=R-[R] where [] is the greatest intege...

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  15. If the middle term in the binomial expansion of (1/x+xsinx)^(10) is eq...

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  16. Find the middle term in the expansion of (x^2+1/(x^2)-2)^ndot

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  17. If the number of terms in the expansion (1+2x-3y+4z)^(n) is 286, then...

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