Question

乘法公式的在认识---因式分解1.已知m+n=3,mn=三分之二,求m平方+(n-mn)平方+2mn-2m平方n的值2.

Answer 1

m^2+(n-mn)^2+2mn-2m^2n

=m^2+n^2-2m^2n+m^2n^2+2mn-2m^2n

=(m+n)^2-2mn^2+m^2n^2-2m^2n

=(m+n)^2-2mn(m+n)+m^2n^2

=(m+n-mn)^2

=(3-2/3)^2

=(7/3)^2

=49/9

证明：

a^2+2b^2+c^2-2ab-2bc=0

a^2-2ab+b^2+b^2-2bc+c^2=0

(a-b)^2+(b-c)^2=0

故：a=b 且 b=c

故：a=b=c,为等边三角形.