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Полина01234
@Полина01234
July 2022
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Если [tex] \frac{ 2x^{2}+2y^{2} }{ x^{2} - y^{2} }=5 [/tex], то чему равно [tex] \frac{2x^{4}+2y^{4}}{ x^{4}-y^{4}} [/tex]
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Segrif
(2x^2 + 2y^2)/(x^2 - y^2) = 5
(x^2 + y^2)/(x^2 - y^2) = 5/2
2x^4 + 2y^4 = (x^2 + y^2)^2 + (x^2 - y^2)^2
x^4 - y^4 = (x^2 + y^2)(x^2 - y^2)
(2x^4 + 2y^4)/(x^4 - y^4) = (x^2 + y^2)^2/(x^2 + y^2)/(x^2 - y^2) +(x^2 - y^2)^2/(x^2 + y^2)/(x^2 - y^2) = (x^2 + y^2)/(x^2 - y^2) + (x^2 - y^2)/(x^2 + y^2) = 5/2 + 2/5 = 2.5 + 0.4 = 2.9
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Полина01234
Это не правильный ответ точно
Полина01234
(x^2 + y^2)^2=х^4+2x^2y^2+y^4
Segrif
Ну, да? А (x^2 - y^2)^2 = x^4 - 2x^2y^2 + y^4. Если сложить, получится 2x^4 + 2y^4
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Answers & Comments
(x^2 + y^2)/(x^2 - y^2) = 5/2
2x^4 + 2y^4 = (x^2 + y^2)^2 + (x^2 - y^2)^2
x^4 - y^4 = (x^2 + y^2)(x^2 - y^2)
(2x^4 + 2y^4)/(x^4 - y^4) = (x^2 + y^2)^2/(x^2 + y^2)/(x^2 - y^2) +(x^2 - y^2)^2/(x^2 + y^2)/(x^2 - y^2) = (x^2 + y^2)/(x^2 - y^2) + (x^2 - y^2)/(x^2 + y^2) = 5/2 + 2/5 = 2.5 + 0.4 = 2.9