已知X不等于0,且M=(X²+2X+1)(X-2X+1),N=(X²+X+1)(x²-X+1),试探究M与N的大小关系急!
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 18:46:36
![已知X不等于0,且M=(X²+2X+1)(X-2X+1),N=(X²+X+1)(x²-X+1),试探究M与N的大小关系急!](/uploads/image/z/1693874-2-4.jpg?t=%E5%B7%B2%E7%9F%A5X%E4%B8%8D%E7%AD%89%E4%BA%8E0%2C%E4%B8%94M%3D%28X%26%23178%3B%2B2X%2B1%EF%BC%89%EF%BC%88X-2X%2B1%EF%BC%89%2CN%3D%EF%BC%88X%26%23178%3B%2BX%2B1%EF%BC%89%EF%BC%88x%26%23178%3B-X%2B1%EF%BC%89%2C%E8%AF%95%E6%8E%A2%E7%A9%B6M%E4%B8%8EN%E7%9A%84%E5%A4%A7%E5%B0%8F%E5%85%B3%E7%B3%BB%E6%80%A5%21)
已知X不等于0,且M=(X²+2X+1)(X-2X+1),N=(X²+X+1)(x²-X+1),试探究M与N的大小关系急!
已知X不等于0,且M=(X²+2X+1)(X-2X+1),N=(X²+X+1)(x²-X+1),试探究M与N的大小关系急!
已知X不等于0,且M=(X²+2X+1)(X-2X+1),N=(X²+X+1)(x²-X+1),试探究M与N的大小关系急!
你题目里面M 应该抄错了,应该是(X²+2X+1)(X²-2X+1)
M-N=(X²+2X+1)(X²-2X+1)-(X²+X+1)(x²-X+1)=[(X²+X+1)+X](X²-2X+1)-(X²+X+1)[(X²-2X+1)+X] 把圆括号的看成整体不展开,就有
=0+X[(X²-2X+1)-(X²+X+1)]=X*(-3X)=-3X² X不等于0,所以,-3X²
题目有问题? M后面的式子X的^2 若果有 M=(x^2+1)^2-4x^2 N=(x^2+1)^2-x^2 显而易见M小于N
(X²+2X+1)(X²-2X+1)M-N=(X²+2X+1)(X²-2X+1)-(X²+X+1)(x²-X+1)=[(X²+X+1)+X](X²-2X+1)-(X²+X+1)[(X²-2X+1)+X] 就有=0+X[(X²-2X+1)-(X²+X+1)]=X*(-3X)=-3X² X不等于0,所以,-3X²<0所以,M