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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`

Text Solution

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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