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Complex Numbers And Quadratic Equations
The sum of the coefficients of all odd degree terms in the expansion of ${\left(x+\sqrt{{x}^{3}1}\right)}^{5}+{\left(x\sqrt{{x}^{3}1}\right)}^{5},(x1)is$
2
1
0
1
A.
2
${\left(x+\sqrt{{x}^{3}1}\right)}^{5}+{\left(x\sqrt{{x}^{3}1}\right)}^{5}\phantom{\rule{0ex}{0ex}}=2[{}^{2}C_{0}{x}^{5}+{}^{5}C_{2}{x}^{3}({x}^{3}1)+{}^{5}C_{4}x({x}^{3}1{)}^{2}]\phantom{\rule{0ex}{0ex}}=2[{x}^{5}+10({x}^{6}{x}^{3})+5x({x}^{6}2{x}^{3}+1)]\phantom{\rule{0ex}{0ex}}=2[{x}^{5}+10{x}^{6}10{x}^{3}+5{x}^{7}10{x}^{4}+5x]\phantom{\rule{0ex}{0ex}}=2[5{x}^{7}+10{x}^{6}+{x}^{5}10{x}^{4}10{x}^{3}+5x]$
Sum of odd degree terms coefficients
= 2(5 + 1 – 10 + 5)
= 2
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