已知(x+y)^2=8,(x-y)^2=5,求3xy与x^2+y^2的值
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已知(x+y)^2=8,(x-y)^2=5,求3xy与x^2+y^2的值已知(x+y)^2=8,(x-y)^2=5,求3xy与x^2+y^2的值已知(x+y)^2=8,(x-y)^2=5,求3xy与x
已知(x+y)^2=8,(x-y)^2=5,求3xy与x^2+y^2的值
已知(x+y)^2=8,(x-y)^2=5,求3xy与x^2+y^2的值
已知(x+y)^2=8,(x-y)^2=5,求3xy与x^2+y^2的值
(x+y)^2=8 (1)
(x-y)^2=5 (2)
==>(1)-(2)==>4xy=3;所以3xy=9/4
(1)+(2)==>2x^2+2y^2=13;所以x^2+y^2=13/2
(x+y)^2-(x-y)^2=4xy=8-5=3
3xy=9/4
,x^2+y^2=(x+y)^2-2xy=8-3/4=29/4
1式+2式=2(x^2+y^2)=13 x^2+y^2=6.5
1式-2式=4xy=3 3xy=2.25
(x+y)^2-(x-y)^2=4xy=8-5=3,(x+y)^2+(x-y)^2=13,即2(x^2+y^2)=13,然后。。。不用我说了吧?
(x+y)^2=8 -> x^2 +y^2+2xy=8 ...a
(x-y)^2=5 -> x^2 +y^2-2xy=5....b
a式-b式=4xy=3 =》 3xy=9/4
把求得的xy值代入a式 得 x^2+y^2=8-2xy=8-2*3/4=13/2
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