已知实数a,b,c,满足a+b+c=1,1/a+b-c + 1/b+c-a +1/c+a-b=1,则abc=_____
人气:441 ℃ 时间:2019-08-19 19:56:20
解答
1/(1-2a)+1/(1-2b)+1/(1-2c)
=(1-2a-2b+4ab+1-2a-2c+4ac+1-2b-2c+4bc)/(1-2a)(1-2b)(1-2c)
=(3-4(a+b+c)+4ab+4ac+4bc)/(1-2a)(1-2b)(1-2c)
=(-1+4ab+4ac+4bc)/((1-2a-2b+4ab)(1-2c))
=(-1+4ab+4ac+4bc)/(1-2c-2a+4ac-2b+4bc+4ab-8abc)
=1
-1+4ab+4ac+4bc=1-2(a+b+c)+4ac+4bc+4ab-8abc
-1=1-2-8abc
abc=0
推荐
- 已知实数a,b,c,满足a+b+c=2,abc=4,(1)a,b,c中最大者的最小值.(2)|a|+|b|+|c|的最小值,并求出取到最小值时a,b,c的值
- 已知实数A,B,C满足A+B+C=0,ABC=8,判断1/A+1/B=1/C的值的正负
- 已知实数a、b、c满足:a+b+c=2,abc=4
- 已知a.b.c是非零实数,且满足b+c/a=c+a/b=a+b/c,求(a+b)(b+c)(c+a)/abc的值
- 已知正实数a,b,c满足abc=1,求证1/a^2+1/b^2+1/c^2≥a+b+c
- 坚持这项工作由一个有经验的工人做She insisted that this work should be done by an exp
- Liu Tao can put some bookson his head.改否定句
- "心灵岛上的灯塔"含义是什么?
猜你喜欢