(1) 化简 (x-c)/(x-a)(x-b)+(b-c)/(a-b)(x-b)+(b-c)/(b-a)(x-a)
来源:学生作业帮 编辑:搜搜考试网作业帮 分类:数学作业 时间:2024/06/05 15:03:43
(1) 化简 (x-c)/(x-a)(x-b)+(b-c)/(a-b)(x-b)+(b-c)/(b-a)(x-a)
(2) 化简(2a-b-c)/(a-b)(a-c)+(2b-c-a)/(b-c)(b-a)+(2c-a-b)/(c-b)(c-a)
(3) 证明,若a+b+c=0,则1/(b方+c方-a方)+1/(c方+a方-b方)+1/(a方+b方-c方)=0
(2) 化简(2a-b-c)/(a-b)(a-c)+(2b-c-a)/(b-c)(b-a)+(2c-a-b)/(c-b)(c-a)
(3) 证明,若a+b+c=0,则1/(b方+c方-a方)+1/(c方+a方-b方)+1/(a方+b方-c方)=0
(1) 化简 (x-c)/(x-a)(x-b)+(b-c)/(a-b)(x-b)+(b-c)/(b-a)(x-a) (x-c)/(x-a)(x-b)+(b-c)/(a-b)(x-b)+(b-c)/(b-a)(x-a) = (x-c)/(x-a)(x-b)+ (b-c)/(a-b)•[1/(x-b)-1/(x-a)] =(x-c)/(x-a)(x-b)+ (b-c)/(a-b)•[(b-a)/(x-b) (x-a)] =(x-c)/(x-a)(x-b)- (b-c)/ /(x-b) (x-a) =(x-b) /(x-a)(x-b) =1//(x-a) (2) 化简(2a-b-c)/(a-b)(a-c)+(2b-c-a)/(b-c)(b-a)+(2c-a-b)/(c-b)(c-a) (2a-b-c)/(a-b)(a-c)+(2b-c-a)/(b-c)(b-a)+(2c-a-b)/(c-b)(c-a) =[(a-b)+(a-c)] /(a-b)(a-c)+[( b-c)+(b-a)]/(b-c)(b-a)+[(c-a)+(c-b)]/(c-b)(c-a) =1/(a-b)+1/(a-c)+1/(b-c)+1/(b-a)+1/(c-a)+1/(c-b) =1/(a-b)+1/(a-c)+1/(b-c)- 1/(a-b)-1/(a-c)-1/(b-c) =0 (3) 证明,若a+b+c=0,则1/(b²+c²-a²)+1/(c²+a²-b²)+1/(a²+b²-c²)=0 因为a+b+c=0,故:a=-(b+c),b=-(a+c),c=-(a+b) 故:b²+c²-a²= b²+c²-[-(b+c)] ²=-2bc c²+a²-b²= c²+a²-[-( a+c)] ²=-2ac;a²+b²-c²=a²+b²-[-( a+b)] ²=-2ab 故:1/(b²+c²-a²)+1/(c²+a²-b²)+1/(a²+b²-c²) =1/(-2bc)+1/(-2ac)+1/(-2ab) =-(a+b+c)/(2abc) =0
(1) 化简 (x-c)/(x-a)(x-b)+(b-c)/(a-b)(x-b)+(b-c)/(b-a)(x-a)
(a-b-c)X( b+c-a)^2X(c-a+b)^3=?
(a-b)(b-c)(c-a)=1,x、y为任意有理数,求(b-a)(x-c)(y-c)+(c-b)(x-a)(y-a)
解方程:(b-c)x^2+(c-a)x+(a-b)=0(b≠c)
已知1/a+1/b+1/c不等于0,解关于x的方程:(x-b-c)/a+(x-c-a)/b+(x-a-b)/c=3
计算或化简(x-1)(x-2)-(2-x)^2(a+b-c)(c+a+b)-(a+b)^
x=(a+b)/c=(b+c)/a=(c+a)/b
若a,b,c满足不等式b+c>a,且(a-b-c)x
证明f(x)=(x-b)(x-c)+(x-c)(x-a)+(x-a)(x-b)必有零点
已知集合A{x|x>5},B={x|x>-1},则A∩B等于 A.{x|x>5},B.{x|x>-1},C{x|-1
已知(c-a-2b)x^2+(a+b-2c)x+(b+c-2a)=0 求x.
(x+a+b)/c+(x+b+c)/a+(x+c+a)/b=-3谢谢了,大神帮忙啊