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AngB1212
@AngB1212
July 2022
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Известно, что x - y = 2 и x * y = 3. Найдите значение выражения y*x^4 - x*y^4.
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Удачник66
Verified answer
X - y = 2; x*y = 3
(x - y)^2 = x^2 - 2xy + y^2
Вычислим дополнительно
x^2 + y^2 = (x - y)^2 + 2xy = 2^2 + 2*3 = 4 + 6 = 10
Подставляем
y*x^4 - x*y^4 = x*y*(x^3 - y^3) = x*y*(x - y)*(x^2 + y^2 + x*y) = 3*2*(10 + 3) = 6*13 = 78
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Answers & Comments
Verified answer
X - y = 2; x*y = 3(x - y)^2 = x^2 - 2xy + y^2
Вычислим дополнительно
x^2 + y^2 = (x - y)^2 + 2xy = 2^2 + 2*3 = 4 + 6 = 10
Подставляем
y*x^4 - x*y^4 = x*y*(x^3 - y^3) = x*y*(x - y)*(x^2 + y^2 + x*y) = 3*2*(10 + 3) = 6*13 = 78