完全平方公式:若x²+y²=25,(x+y)²=49,求(x-y)²的值.
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完全平方公式:若x²+y²=25,(x+y)²=49,求(x-y)²的值.
完全平方公式:若x²+y²=25,(x+y)²=49,求(x-y)²的值.
完全平方公式:若x²+y²=25,(x+y)²=49,求(x-y)²的值.
(x-y)²
=x²-2xy+y²
=(x²+2xy+y²)-4xy
=(x+y)²-2[(x+y)²-(x²+y²)]
=49-2×(49-25)
=49-2×16
=49-32
=17
两式相减可以求出xy,再联系一式可以解出答案
x²+y²=25,(x+y)²=49
(x+y)²-x²+y²=2xy=49-25=24
xy=12
(x-y)²=x²+y²-2xy=25-24=1
(x+y)^2=49 (1)
x^2+y^2 = 25 (2)
(1)-(2)
2xy = 24
xy = 12
(x-y)^2 = (x+y)^2 -4xy = 49-4(12) =1
49-25=24,25-24=1能明白不