Question

Найдите отношение f(kx; ky)/f(x;y) , если f(x;y) = x^4+12x^3y-7x^2y^2+2xy^3-2y^4

Answer 1

f(x;y) = x⁴+12x³y-7x²y²+2xy³-2y⁴ ;

f(kx;ky) =(kx)⁴+12(kx)³(ky)-7(kx)²(ky)²+2(kx)(ky)³-2(ky)⁴=k⁴( x⁴+12x³y-7x²y²+2xy³-2y⁴)=k⁴f(x;y).

f(kx;ky) /f(x;y)=k⁴