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rarararara5
@rarararara5
June 2022
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Найдите a(в степени 3)+b(в степени 3), если известно, что a+b=10 и a+b+a(в степени 2)b+ab(в степени 2)=250
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Удачник66
Verified answer
A + b = 10
a + b + a^2*b + ab^2 = 250
2 уравнение
a + b + ab*(a + b) = (a + b)*(ab + 1) = 250
10(ab + 1) = 250
ab = 24
a^3 + b^3 = (a+b)(a^2-ab+b^2) = (a+b)(a^2+2ab+b^2-3ab) =
= (a+b)((a+b)^2 - 3ab) = 10*(10^2 - 3*24) = 10(100-72) = 280
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Answers & Comments
Verified answer
A + b = 10a + b + a^2*b + ab^2 = 250
2 уравнение
a + b + ab*(a + b) = (a + b)*(ab + 1) = 250
10(ab + 1) = 250
ab = 24
a^3 + b^3 = (a+b)(a^2-ab+b^2) = (a+b)(a^2+2ab+b^2-3ab) =
= (a+b)((a+b)^2 - 3ab) = 10*(10^2 - 3*24) = 10(100-72) = 280