已知x－y=5,xy=2,求：①x²+y²的值；②（x+y）²；③3x²－6xy+3y²

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已知x－y=5,xy=2,求：①x²+y²的值；②（x+y）²；③3x²－6xy+3y²

已知x－y=5,xy=2,求：①x²+y²的值；②（x+y）²；③3x²－6xy+3y²
已知x－y=5,xy=2,求：①x²+y²的值；②（x+y）²；③3x²－6xy+3y²

已知x－y=5,xy=2,求：①x²+y²的值；②（x+y）²；③3x²－6xy+3y²
1、
(x-y)²=5²
x²-2xy+y²=25
x²+y²=25+2xy=29
2、
(x+y)²
=x²+y²+2xy
=29+4
=33
3、
原式=3(x²-2xy+y²)
=3(x-y)²
=3×5²
=75

x2+y2=(x-y)2+2xy=29
（x+y）2=x2+y2+2xy=33
3x2－6xy+3y2=3(x-y)2=75

①x²+y²=29
②（x+y）²=33
③3x²－6xy+3y² =75
过程：①x²+y²=（x-y)²+2xy=25+4=29
②（x+y）²=x²+y²+2xy=29+4=33
③3x²－6xy+3y² =3(x²+y²-2xy)=3(x-y)²=3*25=75

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