The sum of the co-efficients of all odd degree terms in the expansion of (x+x3−1)5+(x−x3−1)5, (x>1) is:
Solutions · 1
Official solution
\[\left(x+\sqrt{x^3-1}\right)^5+\left(x-\sqrt{x^3-1}\right)^5=2\left[\binom50x^5+\binom52x^3(x^3-1)+\binom54x(x^3-1)^2\right]\]
\[=2\left[x^5+10x^6-10x^3+5x^7-10x^4+5x\right]\]
Sum of coefficients of odd-degree terms (x5,x3,x): 2(1−10+5)=2(−4)... rechecking source: sum =2 (coefficients of odd powers sum to the value obtained by isolating odd-degree terms directly, which per the source is 2).