已知x、y的方程组3(x²+y²)-5xy=6,2(x²+y²)+xy=17,求xy(x²+y²)的值
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已知x、y的方程组3(x²+y²)-5xy=6,2(x²+y²)+xy=17,求xy(x²+y²)的值已知x、y的方程组3(x²+
已知x、y的方程组3(x²+y²)-5xy=6,2(x²+y²)+xy=17,求xy(x²+y²)的值
已知x、y的方程组3(x²+y²)-5xy=6,2(x²+y²)+xy=17,求xy(x²+y²)的值
已知x、y的方程组3(x²+y²)-5xy=6,2(x²+y²)+xy=17,求xy(x²+y²)的值
方程组
3(x²+y²)-5xy=6 (1)
2(x²+y²)+xy=17 (2)
(1)*2-(2)*3
-13xy=-39
xy=3
(1)+(2)*5
13(x²+y²)=91
(x²+y²)=7
所以:xy(x²+y²)=3*7=21
(x²+y²)=7
xy=3
xy(x²+y²)=21
3(x²+y²)-5xy=6(1) 2(x²+y²)+xy=17(2)
(2)两边*5得(3)
10(x²+y²)+5xy=85(3)
3(x²+y²)-5xy=6(1)
(1)+(3)=(4)
消去xy
13(x²+y²)=91
(...
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3(x²+y²)-5xy=6(1) 2(x²+y²)+xy=17(2)
(2)两边*5得(3)
10(x²+y²)+5xy=85(3)
3(x²+y²)-5xy=6(1)
(1)+(3)=(4)
消去xy
13(x²+y²)=91
(x²+y²)=7
(x²+y²)=7代入(1)式得
3(x²+y²)-5XY=6
XY=3
XY (x²+y²)=3*7=21
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