将含字母的系数配方成a²,-a²,a²+正数,-a²-正数,判断方程根情况(1)1/4*x²-2mx+5m²+1=0
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将含字母的系数配方成a²,-a²,a²+正数,-a²-正数,判断方程根情况(1)1/4*x²-2mx+5m²+1=0
将含字母的系数配方成a²,-a²,a²+正数,-a²-正数,判断方程根情况
(1)1/4*x²-2mx+5m²+1=0
将含字母的系数配方成a²,-a²,a²+正数,-a²-正数,判断方程根情况(1)1/4*x²-2mx+5m²+1=0
a²+正数=0,无根
-a²-正数=0,无根
1/4*x²-2mx+5m²+1=0
x²-8mx+20m²+4=0
x²-8mx=-20m²-4
x²-8mx+16m²=-20m²-4+16m²
(x-4m)²=-4m²-4
∴方程无解
方程化为:(x/2-2m)^2+m^2+1=0,
(x/2-2m)^2+m^2+1>=1>0,
所以方程无实数根。