Question

若2x〃-(4m-1)x+2m〃+1(〃表示平方)是一个完全平方式,求m的值

Answer 1

设2x^2-(4m-1)x+2m^2+1=(ax+b)^2=a^2x^2-2abx+b^2

比较系数

2=a^2

1-4m=-2ab (1)

2m^2+1=b^2

(1)^2 4m-1=2ab ,16m^2-8m+1=4a^2b^2

16m^2-8m+1=4(2)(2m^2+1)

16m^2-8m+1=8(2m^2+1)=16m^2+8

-8m+1=8

8m=-7

m=-7/8