if a(1 + x/(a^3 + b^3) = b(1 - x/(a^3 + b^3), prove that x = (b-a)(a^2 - ab + b^2)?
2016-08-09 4:02 am
if a(1 + x/(a^3 + b^3) = b(1 - x/(a^3 + b^3), prove that x = (b-a)(a^2 - ab + b^2)
回答 (4)
2016-08-09 4:19 am
✔ 最佳答案
a[1 + x/(a³ + b³)] = b[1 - x/(a³ + b³)]a + ax/(a³ + b³) = b - bx/(a³ + b³)
ax/(a³ + b³) + bx/(a³ + b³) = b - a
(ax + bx)/(a³ + b³) = b - a
(ax + bx) = (b - a)(a³ + b³)
(a + b)x = (b - a)(a³ + b³)
(a + b)x = (b - a)(a + b)(a² - ab + b²)
x = (b - a)(a² - ab + b²) (if a + b ≠ 0)
2016-08-09 4:54 am
Waow, this is really nice, thanks
2016-10-05 8:48 am
Waow, this is really nice, thanks
2016-08-14 5:43 am
a[1 + x/(a^3 + b^3)]=b[1 - x/(a^3 + b^3)]
a+ax/(a^3+b^3)=b-bx/(a^3+b^3)
a(a^3+b^3)+ax=b(a^3+b^3)-bx
(a+b)x=(a^3+b^3)(b-a)
x=(a+b)(a^2-ab+b^2)(b-a)/(a+b)
x=(b-a)(a^2-ab+b^2)
a+ax/(a^3+b^3)=b-bx/(a^3+b^3)
a(a^3+b^3)+ax=b(a^3+b^3)-bx
(a+b)x=(a^3+b^3)(b-a)
x=(a+b)(a^2-ab+b^2)(b-a)/(a+b)
x=(b-a)(a^2-ab+b^2)
收錄日期: 2021-04-18 15:25:18
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https://hk.answers.yahoo.com/question/index?qid=20160808200240AAfIL7T