a^2+b^2=(a+b)^2-2ab=2 ab=-1/2a^3+b^3=(a+b)(a^2-ab+b^2)=1*(2+1/2)=5/2a^4+b^4=(a^2+b^2)^2-2a^2b^2=2^2-1/2=7/2a^7+b^7=(a^3+b^3)(a^4+b^4)-a^3b^4-a^4b^3=35/4-(-1/2)^3*1=69/8
