M1數2條..help me plz!

(1) 解一：算幾不等式 (x^2 + y^2)/2 >= √(x^2y^2)
x^2 + y^2 >= 2xy = 50
x^2 + y^2最小值為50, 相應x^2 = y^2
所以 x^2 + x^2 = 50, x^2 = 25, x= 5 => y = 5
解二 : xy = 25
x = 25/y
代入 N = x^2 + y^2
N = (25/y)^2 + y^2
= (25/y)^2 - 2(25/y)(y) + y^2 + 2(25/y)(y)
= (25/y - y)^2 + 50
當25/y - y = 0 即y = 5時N最小值為50. x = 25/y = 5
(2) 設扇形半徑 = r, 角度為x
周界 = rx + 2r = k
x = (k - 2r)/r = k/r - 2
扇形面積 A = (1/2)r^2x
= (1/2)r2(k/r - 2)
= kr/2 - r^2
= -(r^2 - kr/2 + k^2/16) + k^2/16
= -(r - k/4)^2 + k^2/16
當 r = k/4, 扇形極大面積 = k^2/16

2009-12-26 20:44:35 補充：
N = (25/y - y)^2 + 50
因為 (25/y - y)^2 一定不會小於零,所以它的值最小就是0
若(25/y - y)^2 = 0 則 25/y - y = 0

周界 = 扇形兩條半徑加上弧長
這個周界是鐵線屈曲成的,所以周界= 鐵線長 = k cm