Question

已知代数式 x平方-(m-2)x+2m-7 是一个完全平方式。求m的值

要过程 清楚一点

Answer 1

x^2-(m-2)x+2m-7
x^2-2*(1/2)(m-2)x+[(1/2)(m-2)]^2-[(1/2)(m-2)]^2+2m-7
x^2-2*(1/2)(m-2)x+[(1/2)(m-2)]^2-(1/4)(m^2-4m+4)+2m-7
x^2-2*(1/2)(m-2)x+[(1/2)(m-2)]^2-(1/4)m^2+m-1+2m-7
x^2-2*(1/2)(m-2)x+[(1/2)(m-2)]^2-(1/4)m^2+3m-8
因是完全平方，所以-(1/4)m^2+3m-8=0
m^2-12m+32=0
(m-4)(m-8)=0
m1=4,m2=8

Answer 2

完全平方式Δ=0
所以 （m-2)2-4*(2m-7)=0
解得 m=4 或 m=8