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Find the value of (sqrt(2)+1)^6-(sqrt(2)...

Find the value of `(sqrt(2)+1)^6-(sqrt(2)-1)^6dot`

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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-BINOMIAL THEOREM-Exercise 8.1
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  2. If the coefficient of 4th term in the expansion of (a+b)^n is 56, then...

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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-(10...

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  6. Prove that sum(r=0)^(n) (-1)^(r)""^(n)C(r)[1/(2^(r))+(3^(r))/(2^(2r...

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  7. Find n in the binomial (2 3+1/(3 3))^n , if the ration 7th term from t...

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  8. If the coefficients of (r-5)^(t h) and (2r-1)^(t h) terms in the expan...

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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)^6-(sqrt(2)-1)^6dot

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  13. If 1/(sqrt(4x+1)){((1+sqrt(4x+1))/2)^n-((1-sqrt(4x+1))/2)^n}=a0+a1x t...

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  14. Let R=(5sqrt(5)+11)^(2n+1)a n df=R-[R]w h e r e[] denotes the greatest...

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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^n)dot

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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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