已知(x+y)^2=324,(x-y)^2=16,求xy和x^2+y^2的值

来源:学生作业帮助网 编辑:六六作业网 时间:2024/05/27 13:34:58
已知(x+y)^2=324,(x-y)^2=16,求xy和x^2+y^2的值已知(x+y)^2=324,(x-y)^2=16,求xy和x^2+y^2的值已知(x+y)^2=324,(x-y)^2=16

已知(x+y)^2=324,(x-y)^2=16,求xy和x^2+y^2的值
已知(x+y)^2=324,(x-y)^2=16,求xy和x^2+y^2的值

已知(x+y)^2=324,(x-y)^2=16,求xy和x^2+y^2的值
(x+y)^2=324,==>X^2+Y^2+2XY=324 (1)
(x-y)^2=16 ==>X^2+Y^2-2XY=16 (2)
(1)+(2):2(X^2+Y^2)=340 ==>X^2+Y^2=170
(1)-(2):4XY=308 ===>XY=154