一条分式数学题,已知a+b+c=0,试求(a^2/2a^2+bc)+(b^2/2b^2+ac)+(c^2/2c^2+ab)的值.
来源:学生作业帮助网 编辑:作业帮 时间:2024/08/26 16:20:30
![一条分式数学题,已知a+b+c=0,试求(a^2/2a^2+bc)+(b^2/2b^2+ac)+(c^2/2c^2+ab)的值.](/uploads/image/z/611430-6-0.jpg?t=%E4%B8%80%E6%9D%A1%E5%88%86%E5%BC%8F%E6%95%B0%E5%AD%A6%E9%A2%98%2C%E5%B7%B2%E7%9F%A5a%2Bb%2Bc%3D0%2C%E8%AF%95%E6%B1%82%28a%5E2%2F2a%5E2%2Bbc%29%2B%28b%5E2%2F2b%5E2%2Bac%29%2B%28c%5E2%2F2c%5E2%2Bab%29%E7%9A%84%E5%80%BC.)
一条分式数学题,已知a+b+c=0,试求(a^2/2a^2+bc)+(b^2/2b^2+ac)+(c^2/2c^2+ab)的值.
一条分式数学题,
已知a+b+c=0,试求(a^2/2a^2+bc)+(b^2/2b^2+ac)+(c^2/2c^2+ab)的值.
一条分式数学题,已知a+b+c=0,试求(a^2/2a^2+bc)+(b^2/2b^2+ac)+(c^2/2c^2+ab)的值.
已知a+b+c=0,试求 a^2/[2a^2+bc]+b^2/[2b^2+ac]+c^2/[2c^2+ab]的值
a+b+c=0=====>a+b=-c
a^3+b^3=(a+b)(a^2-ab+b^2)=-c[(a+b)^2-3ab]=-c(c^2-3ab)=3abc-c^3
a^2/[2a^2+bc]+b^2/[2b^2+ac]
=[a^2(2b^2+ac)+b^2(2a^2+bc)]/[(2a^2+bc)(2b^2+ac)]
=[4a^2b^2+c(a^3+b^3)]/[4a^2b^2+2c(a^3+b^3)+abc^2]
=[4a^2b^2+c(3abc-c^3)]/[4a^2b^2+2c(3abc-c^3)+abc^2]
=[4a^2b^2+3abc^2-c^4]/[4a^2b^2+6abc^2-2c^4+abc^2]
=[4a^2b^2+3abc^2-c^4]/[4a^2b^2+7abc^2-2c^4]
=[(4ab-c^2)(ab+c^2)]/[(4ab-c^2)(ab+2c^2)]
=(ab+c^2)/(ab+2c^2)
所以:a^2/[2a^2+bc]+b^2/[2b^2+ac]+c^2/[2c^2+ab]
=(ab+c^2)/(ab+2c^2)+c^2/(2c^2+ab)
=(ab+c^2+c^2)/(2c^2+ab)
=(2c^2+ab)/(2c^2+ab)
=1