如果x-y=m,y-z=n,那么x² + y² +z² -xy-yz-zx的值等于( )A.mn B.(m²+n²)n C.m²+n²+mn D.mn(m+n)虽然是填空题,还是希望各位能写出过程来,毕竟我要弄懂啊,.
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![如果x-y=m,y-z=n,那么x² + y² +z² -xy-yz-zx的值等于( )A.mn B.(m²+n²)n C.m²+n²+mn D.mn(m+n)虽然是填空题,还是希望各位能写出过程来,毕竟我要弄懂啊,.](/uploads/image/z/2982922-34-2.jpg?t=%E5%A6%82%E6%9E%9Cx-y%3Dm%2Cy-z%3Dn%2C%E9%82%A3%E4%B9%88x%26sup2%3B+%2B+y%26sup2%3B+%2Bz%26sup2%3B+-xy-yz-zx%E7%9A%84%E5%80%BC%E7%AD%89%E4%BA%8E%EF%BC%88+%EF%BC%89A.mn+B.%28m%26sup2%3B%2Bn%26sup2%3B%29n+C.m%26sup2%3B%2Bn%26sup2%3B%2Bmn+D.mn%28m%2Bn%29%E8%99%BD%E7%84%B6%E6%98%AF%E5%A1%AB%E7%A9%BA%E9%A2%98%2C%E8%BF%98%E6%98%AF%E5%B8%8C%E6%9C%9B%E5%90%84%E4%BD%8D%E8%83%BD%E5%86%99%E5%87%BA%E8%BF%87%E7%A8%8B%E6%9D%A5%2C%E6%AF%95%E7%AB%9F%E6%88%91%E8%A6%81%E5%BC%84%E6%87%82%E5%95%8A%2C.)
如果x-y=m,y-z=n,那么x² + y² +z² -xy-yz-zx的值等于( )A.mn B.(m²+n²)n C.m²+n²+mn D.mn(m+n)虽然是填空题,还是希望各位能写出过程来,毕竟我要弄懂啊,.
如果x-y=m,y-z=n,那么x² + y² +z² -xy-yz-zx的值等于( )
A.mn B.(m²+n²)n C.m²+n²+mn D.mn(m+n)
虽然是填空题,还是希望各位能写出过程来,毕竟我要弄懂啊,.
如果x-y=m,y-z=n,那么x² + y² +z² -xy-yz-zx的值等于( )A.mn B.(m²+n²)n C.m²+n²+mn D.mn(m+n)虽然是填空题,还是希望各位能写出过程来,毕竟我要弄懂啊,.
C.m²+n²+mn
x-z=m+n
x² + y² +z² -xy-yz-zx
=1/2[(x-y)^2+(y-z)^2+(x-z)^2]
=1/2[m^2+n^2+(m+n)^2]
=m^2+n^2+mn
x-y=m,y-z=n,
x-z=m+n,
原式=[(x-y)^2+(x-z)^2+(y-z)^2]/2
C
x-y=m,(1)
y-z=n(2)
(1)+(2)
x-z=m+n
(2x² + 2y² +2z² -2xy-2yz-2zx)/2
=(x²-2xy+y²+y²-2yz+z²+x²-2xz+z²)/2
=【(x-y)²+(y-z)²+(x-...
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x-y=m,(1)
y-z=n(2)
(1)+(2)
x-z=m+n
(2x² + 2y² +2z² -2xy-2yz-2zx)/2
=(x²-2xy+y²+y²-2yz+z²+x²-2xz+z²)/2
=【(x-y)²+(y-z)²+(x-z)²】/2
=【m²+n²+(m+n)²】/2
=(2m²+2n²+2mn)/2
=m²+n²+mn
z
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x-y=m,y-z=n,x-z=m+n把(x-y)、(y-z)、(x-z)分别平方,再相加,得出的结果再除以2.所以选C