已知x-y=2+a,y-z=2-a,且a^2=7,试求x^2+y^2+z^2-xy-yz-zx的值.
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![已知x-y=2+a,y-z=2-a,且a^2=7,试求x^2+y^2+z^2-xy-yz-zx的值.](/uploads/image/z/7085788-52-8.jpg?t=%E5%B7%B2%E7%9F%A5x-y%3D2%2Ba%2Cy-z%3D2-a%2C%E4%B8%94a%5E2%3D7%2C%E8%AF%95%E6%B1%82x%5E2%2By%5E2%2Bz%5E2-xy-yz-zx%E7%9A%84%E5%80%BC.)
已知x-y=2+a,y-z=2-a,且a^2=7,试求x^2+y^2+z^2-xy-yz-zx的值.
已知x-y=2+a,y-z=2-a,且a^2=7,试求x^2+y^2+z^2-xy-yz-zx的值.
已知x-y=2+a,y-z=2-a,且a^2=7,试求x^2+y^2+z^2-xy-yz-zx的值.
x^2+y^2+z^2-xy-yz-zx X=2+A+Y Z=Y-2-A A=√7
=(x^2+y^2+z^2-xy-yz-zx)×2÷2
=(2x^2+2y^2+2z^2-2xy-2yz-2zx)÷2
=((X-Y)^2+(X-Z)^2+(Y-Z)^2)÷2
=((2+A)^2+(2+A+Y-Y+2+A)^2+(2-A)^2)÷2
= ((2+A)^2+(4+2A)^2)+(2-A)^2)÷2
= ((4-A^2)^2+(4+2A)^2))÷2
=(4-√7)^2+(4+2√7)^2)÷2
=(16-7+16+28)÷2
=43÷2
=21.5
a方+12