Задача 52487 11.1.37. Даны функции [m] f(x;y) = x^2 +...

vk477579336

2020-06-16 18:08:09

11.1.37. Даны функции [m] f(x;y) = x^2 + y^2 [/m] и [m] g(x;y) = x^2 - y^2 [/m]. Найти:
а) [m] f(g(x;y); y^2) [/m];
б) [m] g(f(x;y); g(x;y)) [/m].

sova

2020-06-16 20:18:16

★

a) f(g(x;y);y^2)=g^2(x;y)+(y^2)^2=(x^2-y^2)^2+y^2=x^2-2x^2y^2+2y^4
б) g(f(x;y);g(x;y))=(x^2+y^2)^2-(x^2-y^2)^2=(x^2+y^2-x^2+y^2)(x^2+y^2+x^2-y^2)=2y^2*2x^2=4x^2y^2