已知(x+y)^2=1,(x-y)^2=49,求x^2+y^2与xy的值
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已知(x+y)^2=1,(x-y)^2=49,求x^2+y^2与xy的值
已知(x+y)^2=1,(x-y)^2=49,求x^2+y^2与xy的值
已知(x+y)^2=1,(x-y)^2=49,求x^2+y^2与xy的值
(x+y)^2=1,
(x-y)^2=49
两式相加得:
2(x²+y²)=50
x²+y²=25
两式相减得:
4xy=-48
xy=-12
x²+y²=[﹙x+y﹚²+﹙x-y﹚²]/2=﹙1+49﹚/2=25
xy=[﹙x+y﹚²-﹙x-y﹚²]/4=50/4=22.5
x^2+y^2=25;
xy=-12
(x+y)^2=1,
即x^2+2xy+y^2=1 ①
(x-y)^2=49
即x^2-2xy+y^2=49 ②
①+②,得
2(x^2+y^2)=50
x^2+y^2=25
代入 ①,得
25+2xy=1
2xy=-24
xy=-12
(x+y)^2=1 ,(x-y)^2=49
x^2+y^2+2xy=1 x^2+y^2-2xy=49
两式相加得2x^2+2y^2=50
x^2+y^2=25
两式相减得4xy=-48
xy=-12
(x+y)^2=x 2;+2xy+y 2;=49 (x-y)^2=x 2;-2xy+y 2;=1 所以 x 2;+y 2;=[(x+y) 2;+(x-y) 2;]÷2=(49+1)÷2=25 xy=[
两式子相减得到XY的值,再代入其中一个式子就得到另一个要求的了
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