若多项式(2mx²-x²+3x+1)-(5x²-4y²+3x)的值与x无关,求2m³-【3m²+(4m-5)+m】的值
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![若多项式(2mx²-x²+3x+1)-(5x²-4y²+3x)的值与x无关,求2m³-【3m²+(4m-5)+m】的值](/uploads/image/z/224757-45-7.jpg?t=%E8%8B%A5%E5%A4%9A%E9%A1%B9%E5%BC%8F%EF%BC%882mx%26%23178%3B-x%26%23178%3B%2B3x%2B1%EF%BC%89-%EF%BC%885x%26%23178%3B-4y%26%23178%3B%EF%BC%8B3x%EF%BC%89%E7%9A%84%E5%80%BC%E4%B8%8Ex%E6%97%A0%E5%85%B3%2C%E6%B1%822m%26%23179%3B-%E3%80%903m%26%23178%3B%2B%EF%BC%884m-5%EF%BC%89%2Bm%E3%80%91%E7%9A%84%E5%80%BC)
若多项式(2mx²-x²+3x+1)-(5x²-4y²+3x)的值与x无关,求2m³-【3m²+(4m-5)+m】的值
若多项式(2mx²-x²+3x+1)-(5x²-4y²+3x)的值与x无关,求2m³-【3m²+(4m-5)+m】的值
若多项式(2mx²-x²+3x+1)-(5x²-4y²+3x)的值与x无关,求2m³-【3m²+(4m-5)+m】的值
(2mx²-x²+3x+1)-(5x²-4y²+3x)
=(2m-1)x^2+3x+1-5x^2+4y^2-3x
=(2m-1-5)x^2+4y^2+1
=(2m-6)x^2+4y^2+1
因为多项式(2mx²-x²+3x+1)-(5x²-4y²+3x)的值与x无关,
所以2m-6=0,
m=3
2m³-【3m²+(4m-5)+m】
=2m³-3m²-(4m-5)-m
=-m²-5m+5
=-9-15+5
=-19
1
合并同类项 可得原多项式为 (2m-6)x²+1+4y²
其值与x无关可知 x²的系数为0 2m-6=0 m=3
2m³-【3m²+(4m-5)+m】=17
由题意得:因为(2mx²-x²+3x+1)-(5x²-4y²+3x)的值与x无关
(2mx²-x²+3x+1)-(5x²-4y²+3x)=(2m-1-5)x^2+(3-3)x+4y^2+1=(2m-6)x^2+4y^2+1
所以2m-6=0得m=3
2m³-【3m²+(4m-5)+m】=2x3^3-3x3^2-5x3+5=17
17
由题意有2m-6=0,
m=3
∴原式=17