m为何值时,方程组x²+y²=20;x+y=m有两组相同的实数解,并求出这时方程组的解解方程(5-x)²+(1-y)²=z².;(7-x)²+(-3-y)²=z².;(2-x)²+(-8-y)²=z².
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m为何值时,方程组x²+y²=20;x+y=m有两组相同的实数解,并求出这时方程组的解解方程(5-x)²+(1-y)²=z².;(7-x)²+(-3-y)²=z².;(2-x)²+(-8-y)²=z².
m为何值时,方程组x²+y²=20;x+y=m有两组相同的实数解,并求出这时方程组的解
解方程(5-x)²+(1-y)²=z².;(7-x)²+(-3-y)²=z².
;(2-x)²+(-8-y)²=z².
m为何值时,方程组x²+y²=20;x+y=m有两组相同的实数解,并求出这时方程组的解解方程(5-x)²+(1-y)²=z².;(7-x)²+(-3-y)²=z².;(2-x)²+(-8-y)²=z².
x²+y²=20 ①
x+y=m ②
由②得:y=m-x
代入①:x²+(m-x)²=20
x²+m²-2mx+x²=20
2x²-2mx+m²-20=0
因为方程有两组相同的实数解
所以Δ=4m²-4*2*(m²-20)=0
m²-2m²+40=0
m²=40
m=2√10或m=-2√10
当m=2√10时,x1=x2=2m/4=√10,y1=y2=m-x=√10
当m=-2√10时,x1=x2=2m/4=-√10,y1=y2=m-x=-√10
当x+y = m 与圆相切时 此时x = y = +/-根号(10) m = +/-2根号(10)