>>9

43/3 = a とおく。

0 = x^3 + y^3 - (xx+42xy+yy)

= {x+y+(42-2a)}{xx-xy+yy -a(x+y) +a(42-2a)} - a(42-2a)^2

= X^3 + Y^3 +42(XX-XY+YY) -a(X+Y) -aa(4a-42)

= (X+Y+42)(XX-XY+YY -a) - a(42-2a)^2,

ここに、X = x-a,　Y = y-a,

漸近線：　x+y+(42-2a)=0　(X+Y+42=0)

>>33

4(x^3 + y^3) - (x+y)^3 = (x+y){4(xx-xy+yy) -(x+y)^2}
　= (x+y){3(x-y)^2}
　≧ 0