Question

已知实数x,y,满足x^2/4+y^2=1,求y/(x+3)的取值范围

Answer 1

设Y/(X+3)=A 则有 Y=A(X+3)

代入

X^2/4+A^2(X+3)^2=1

(1/4+A^2)X^2+6A^2X+9A^2-1=0

因为方程有解,其判别式

(6A^2)^2-4(9A^2-1)(1/4+A^2)>=0

36A^4-4(9A^2/4+9A^4-1/4-A^2)>=0

5A^2/4-1/4