Формула квадрата суммы: (a + b)^2 = a^2 + 2ab + b^2 = (a^2 + ab + b^2) + ab
a^2 + ab + b^2 = (a + b)^2 - ab
Тут a = x^2, b = y^2:
x^4 + x^2 y^2 + y^4 = (x^2 + y^2)^2 - x^2 y^2 = (x^2 + y^2)^2 - (xy)^2 = 6^2 - 2^2 = 36 - 4 = 32
<span>x : y=4 : 9 → х = 4у/9
</span><span>y : z = 15 : 8/3 → z = 8y/45
4y/9 + y + 8y/45 = 219
73y/45 = 219
y = 135
x = 4y/9 = 4 · 135 : 9 = 60
z = 8 · 135 : 45 = 24
Проверка: 60 + 135 + 24 = 219
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92/45. удачи :)))))))))))))))