已知x+y=15,x^2+y^2=133,求x^2-xy+y^2的值.
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已知x+y=15,x^2+y^2=133,求x^2-xy+y^2的值.
已知x+y=15,x^2+y^2=133,求x^2-xy+y^2的值.
已知x+y=15,x^2+y^2=133,求x^2-xy+y^2的值.
因为x+y=15,所以(x+y)^2=225=x^2+y^2+2xy
又因为x^2+y^2=133,可得2xy=92,xy=92/2=46
则x^2-xy+y^2=133-46=87
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(x+y)^2=x^2+2xy+y^2=15*15=225
其中x^2+y^2=133
可知2xy=(x+y)^2-x^2+y^2=225-133=92
xy=46
最后x^2-xy+y^2=133-46=87
x+y=15
(x+y)²=15²
x²+2xy+y²=225
133+2xy=225
2xy=92
xy=46
x²-xy+y²
=133-46
=87
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