已知x+y=5,xy=3.求：①x²+y²；②（x-y）²

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

已知x+y=5,xy=3.求：①x²+y²；②（x-y）²
x^2+y^2=(x+y)^2-2xy=5^2-2*3=25-6=19 (x-y)^2=(x+y)^2-4xy=5^2-3*4=25-12=13

x+y=5
(x+y)²=25
x²+2xy+y²=25
x²+y²+2×3=25
x²+y² = 19
（x-y）²
=x²+y²-2xy
=19-2×3
=13

x²+y²
=x²+y²+2xy-2xy
=(x+y)²-2xy
=5²-2×3
=25-6
=19
(x-y)²
=x²+y²-2xy
=19-2×3
=19-6
=13下一题：已知（a+b）²=30,(a-b)
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x²+y²
=x²+y²+2xy-2xy
=(x+y)²-2xy
=5²-2×3
=25-6
=19
(x-y)²
=x²+y²-2xy
=19-2×3
=19-6
=13

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x+y=5得x²+y²+2xy=25 xy=3 x²+y²=19
（x-y）²=x²+y²-2xy=（x+y）²-4xy=25-24=1