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数学
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已知实数x,y,z满足:x+y-6=0,z²+9=xy,则x²+1/3y²=?
A.6
B.12
C.18
D.36
人气:499 ℃ 时间:2019-10-09 12:40:51
解答
xy=z²+9>0,x,y均不为0,且同号.
x+y-6=0 x+y=6
由均值不等式得(x+y)²≥4xy
36≥4(z²+9)
z²≤0
又平方项恒非负,因此只有z=0 其实本题的关键就在这一步判断上了.
x+y=6 xy=9
x,y是方程m²-6m+9=0的两根.
(m-3)²=0
m=3
x=y=3
x²+(1/3)y²=3²+(1/3)·3²=9+3=12
选B.
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