Mathematics - Binomial Theorem Question with Solution | TestHub

Since ${\left(x+\sqrt{x^2-1}\right)}^8+{\left(x-\sqrt{x^2-1}\right)}^8$ $\begin{array}{r}=2\{{}^8{C}_0{x}^8+{}^8{C}_2{x}^6\left(x^2-1\right)+{}^8{C}_4{x}^4{\left(x^2-1\right)}^2\\ +{}^8{C}_6{x}^2{\left(x^2-1\right)}^3+{}^8{C}_8{x}^0{\left(x^2-1\right)}^4\}\end{array}$ So coefficient of highest power of $x$ $=2\left\{{}^8{C}_0+{}^8{C}_2+{}^8{C}_4+{}^8{C}_6+{}^8{C}_8\right\}$ $=(1+1{)}^8+(1-1{)}^8=2^8=256$