Question

若2x²-(4m-1)x+2m²+1是一个完全平方式。则m=

Answer 1

2x^2-(4m-1)x+2m^2+1
=2[x^2-(2m-1/2)x+m^2+1/2]
=2[x-(m-1/4)]^2+m+7/8 是完全平方式
则m+7/8=0
所以m=-7/8

Answer 2

解：2x²-(4m-1)x+2m²+1
＝(√2x)²-2*(4m-1)/(2√2)*√2x+2m²+1
所以［(4m-1)/(2√2)］²＝2m²+1
(16m²-8m+1)/8=2m²+1
16m²-8m+1=16m²+8
-8m=7
m=-7/8