谁会?=,=已知an-bm不等于0,a不等于0 ax^2+bx+c=0 mx^2+nx+p=0求证(cm-ap)^2=(bp-cn)(an-bm).

谁会?=,=已知an-bm不等于0,a不等于0 ax^2+bx+c=0 mx^2+nx+p=0求证(cm-ap)^2=(bp-cn)(an-bm).
谁会?=,=
已知an-bm不等于0,a不等于0 ax^2+bx+c=0 mx^2+nx+p=0
求证(cm-ap)^2=(bp-cn)(an-bm).

谁会?=,=已知an-bm不等于0,a不等于0 ax^2+bx+c=0 mx^2+nx+p=0求证(cm-ap)^2=(bp-cn)(an-bm).
证明：
ax^2 +bx+c=0.(1)
mx^2 +nx+p=0.(2)
由(2)*a-(1)*m,整理得
(an-bm)x=cm-ap
∵ an-bm≠0,
∴x=(cm-ap)/(an-bm)代入（1）,得
a[(cm-ap)/(an-bm)]^2+b(cm-ap)/(an-bm)+c=0
上方程两边同时*（an-bm）^2 ,得
a(cm-ap)^2+b(cm-ap)*（an-bm)+c(an-bm)^2 =0
a(cm-ap)^2+（an-bm)*[b(cm-ap）+c(an-bm)] =0
a(cm-ap)^2+（an-bm)*（bcm-abp+acn-bcm) =0
a(cm-ap)^2+（an-bm)*（-abp+acn) =0
a(cm-ap)^2+a（an-bm)*（-bp+cn) =0
∵a≠0
∴(cm-ap)^2+（an-bm)*（-bp+cn) =0
∴(cm-ap)^2=（bp-cn)*（an-bm)

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