Q2014/104) find the degree of polynomial $(x+\sqrt{x^3-1})^7 + (x-\sqrt{x^3-1})^7$

We have

$(a+b)^7=a^7+7a^6b+21a^5b^2+35a^4b^3+35a^3b^4+21a^2b^5+7ab^6+b^7$
also  
$(a-b)^7=a^7-7a^6b+21a^5b^2-35a^4b^3+35a^3b^4-21a^2b^5+7ab^6-b^7$

so $(a+b)^7 + (a-b)^7= 2a^7+42a^5b^2+70a^3b^4+14ab^6$

So $(x+\sqrt{x^3-1})^7 + (x-\sqrt{x^3-1})^7$
= $2 x^7+42x^5(x^3-1)+70x^3(x^3-1)^2+14x(x^3-1)^3$

now the term with highest power of x is $x^{10}$ and so 10 is degree of polynomial