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Find the degree of the polynomial 1/(sqr...

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

Text Solution

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`(1)/(sqrt(4x+1)){((1+sqrt(4x+1))/(2))^(7) - ((1-sqrt(4x+1))/(2))^(7)}`
` = (2)/(2^(7)sqrt(4x+1)) [.^(7)C_(1)sqrt(4x+1) + .^(7)C_(3)(sqrt(4x+1))^(3) + .^(7)C_(5)(sqrt(4x+1))^(5) + .^(7)C_(7)(sqrt(4x+1))^(7)]`
` = (1)/(2^(6))[.^(7)C_(1)+.^(7)C_(3)(4x+1)+.^(7)C_(5)(4x+1)^(2)+.^(7)C_(7)(4x+1)^(3)]`
Clearly the degree of the polynomial is 3.
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