Question

宣(*'へ'*)

求解owo!

(3) 設x,y為實數,滿足 |x + 1| ≤ 2 且 |y - 5| ≤3,求xy-3x+ 2y + 1
之範圍

Answer 1

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|x+1|<=2
=> -2 <= x+1 <= 2
=> -3 <= x <= 1

|y-5|<=3
=> -3 <= y-5 <= 3
=> 2 <= y <= 8

-3×8 <= xy <= 1×8
-24-3+2×2+1 <= xy-3x+2y+1 <= 8+9+16+1

Ans. -22 ~ 34