已知实数x,y满足x⼀y=x-y,若x>0,则x最小值为()

A 2 B 6 C 4 D8
2025-02-26 18:04:15
推荐回答(3个)
回答1:

x/y=x-y, x=y+x/y≥2√(y*x/y)=2√x;∵x>0∴不等式平方得x^2≥4x ∴x≥4 选C

回答2:

x/y=x-y, x=xy-y^2, (y-1)x=y^2,由重要不等式: x=y^2/(y-1)=y-1+1/(y+1)+2>=4

回答3:

x/y=x-y
x=(x-y)y
x=xy-y*y
x-xy=-y*y
x(1-y)=-y*y
x=y*y/(y-1)=((y-1)^2+2(y-1)+1)/(y-1)≥y-1+2+1/(y-1)≥4