已知(x+y)^2=25,(x-y)^2=9,求xy与x^2+y^2的值

来源：学生作业帮助网编辑：六六作业网时间：2024/12/26 03:49:16

已知(x+y)^2=25,(x-y)^2=9,求xy与x^2+y^2的值已知(x+y)^2=25,(x-y)^2=9,求xy与x^2+y^2的值已知(x+y)^2=25,(x-y)^2=9,求xy与x

已知(x+y)^2=25,(x-y)^2=9,求xy与x^2+y^2的值
已知(x+y)^2=25,(x-y)^2=9,求xy与x^2+y^2的值

已知(x+y)^2=25,(x-y)^2=9,求xy与x^2+y^2的值
(x+y)²=25
(x-y)²=9
展开得
x²+2xy+y²=25
x²-2xy+y²=9
化为
(x²+y²)+2(xy)=25
(x²+y²)-2(xy)=9
两式相加得
2(x²+y²)=34
x²+y²=17,所以xy=4

(x+y)^2=25
x^2+2xy+y^2=25
(x-y)^2=9
x^2-2xy+y^2=9
相加
2x^2+2y^2=25+9
x^2+y^2=17
xy=[25-(x^2+y^2)]/2=(25-17)/2=4

(x+y)^2=x^2+2xy+y^2=25......(1)
(x-y)^2=x^2-2xy+y^2=9......(2)
[(1)+(2)]/2=>x^2+y^2=17
[(1)-(2)]/4=>xy=4

xy=[(x+y)^2-(x-y)^2]/4=(25-9)/4=4
x^2+y^2=[(x+y)^2+(x-Y)^2]/2=(25+9)/2=17

xy=4;x^2+y^2=17

已知X*X+Y*Y+6X-8Y+25=0 求（Y/X)+(X/Y)-2=? 已知x-y/x+y=3,求代数式5(x-y)/x+y-x+y/2(x-y) 已知x-y=3,求[（x+y)(x-y)-(x-y)^2+2y(x-y)]除以的值已知3x =2y 求x/x+y+y/x-y-y²/x²-y² 已知f(x+y,y/x)=x^2-y^2,则f(x,y)= 已知|x|=2,|y|=3,|x+y|=-(x+y)求x-y 已知x≠y,x^2-x=y^2-y,求x+y的值. 已知x>0,Y>0,如何证x^2/y+y^2/x>=x+y 已知x+y=2,则(x+y)^2-10x-10y+25=___. 已知x+y=2,则（x+y)2次方-10x-10y+25= x-y/x-x+y/y-(x+y)(x-y)/y² y/x=2 已知x+y=a,2x-y=-2a,求[（x/y-y/x)/(x+y)-x(1/x-1/y)]/[(x+1)/y]的值已知x^2+y^2=25,x+y=7,且x>y,则x-y 的值等于已知x^2+y^2=25,x+y=7,且x小于y求x-y的值已知实数x,y满足(x+y)^2=1,(x-y)^2=25,求x,y的值已知x^2+y^2-6x-8y+25=0,求分式y/x - x/y的值已知x^2+y^2-6x-8y+25=0 求y/x-x/y的值已知x,y满足x^2+y^2-6x+8y+25=0,求y^x的值