如图，某居民小区要在一块一边靠墙（墙长35m）的空地上修建一个矩形花园ABCD，花园的一边靠墙，另三边用
\u5982\u56fe\u6240\u793a\uff1a\u67d0\u5c45\u6c11\u5c0f\u533a\u8981\u5728\u4e00\u5757\u8981\u8fb9\u9760\u5899\uff08\u5899\u957f25m\uff09\u7684\u7a7a\u5730\u4e0a\u4fee\u5efa\u4e00\u4e2a\u77e9\u5f62\u82b1\u56edABCD\uff0c\u82b1\u56ed\u7684\u4e00\u8fb9\u9760\u5899\uff0c\u53e6\u4e09\uff081\uff09\u8bbeBC\u957f\u4e3axm\uff080\uff1cx\u226425\uff09\uff0c\u5219AB\u7684\u957f\u4e3a40?x2m\uff0c\u4f9d\u9898\u610f\uff0c\u5f97\uff1a40?x2?x=182\uff0c\u89e3\u5f97x1=14\uff0cx2=26\uff08\u4e0d\u5408\u9898\u610f\u820d\u53bb\uff09\uff0c40?x2=40?142=13\uff0c\u5219AB\u7684\u957f\u4e3a13m\uff0cBC\u7684\u957f\u4e3a14m\uff0e\u6545\u6211\u7684\u8bbe\u8ba1\u65b9\u6848\u662f\u957f14\u7c73\uff0c\u5bbd13\u7c73\uff0e\uff082\uff09\u8bbeBC\u957f\u4e3axm\uff080\uff1cx\u226425\uff09\uff0c\u5219AB\u7684\u957f\u4e3a40?x2m\uff0c\u4f9d\u9898\u610f\uff0c\u5f97\uff1a40?x2?x=250\uff0c\u5316\u7b80\u5f97x2-40x+500=0\uff0c\u25b3=\uff08-40\uff092-4\u00d7500=-400\uff1c0\uff0c\u6545\u65b9\u7a0b\u65e0\u89e3\uff0c\u6545\u4e0d\u80fd\u4f7f\u5f97\u82b1\u56ed\u7684\u9762\u79ef250m2\uff0e
\uff081\uff09 \uff080\uff1cx\u226415\uff09;\uff082\uff09\u82b1\u56ed\u9762\u79ef\u4e0d\u80fd\u8fbe\u5230200 ,\u7406\u7531\u89c1\u89e3\u6790;\uff083\uff09\u5f53x=15\u65f6,\u82b1\u56ed\u9762\u79ef\u6700\u5927\uff0e \u8bd5\u9898\u5206\u6790\uff1a\uff081\uff09\u5df2\u77e5\u77e9\u5f62\u7684\u957f\u548c\u5468\u957f\u53ef\u8868\u793a\u5bbd,\u8fd0\u7528\u516c\u5f0f\u8868\u793a\u9762\u79ef,\u6839\u636e\u5899\u5bbd\u5f97x\u7684\u53d6\u503c\u8303\u56f4;\uff082\uff09\u6c42\u5f53y=200\u65f6x\u7684\u503c,\u6839\u636e\u81ea\u53d8\u91cf\u7684\u53d6\u503c\u8303\u56f4\u56de\u7b54\u95ee\u9898;\uff083\uff09\u6839\u636e\u51fd\u6570\u5173\u7cfb\u5f0f\u8fd0\u7528\u6027\u8d28\u6c42\u6700\u503c\uff0e\u8bd5\u9898\u89e3\u6790\uff1a\uff081\uff09\u6839\u636e\u9898\u610f\u5f97\uff1a \uff080\uff1cx\u226415\uff09\uff082\uff09\u4e0d\u80fd\u2235 ,\u89e3\u5f97\uff1a \uff1e15,\u2234\u82b1\u56ed\u9762\u79ef\u4e0d\u80fd\u8fbe\u5230200 ;\uff083\uff09\u2235 = \u2234\u51fd\u6570\u56fe\u8c61\u9876\u70b9\u4e3a\uff0820,200\uff09\u4e14\u5f00\u53e3\u5411\u4e0b,\u2234\u5f53x\uff1c20\u65f6,y\u968fx\u7684\u589e\u5927\u800c\u589e\u5927,\u800c0\uff1cx\u226415\u2234\u5f53x=15\u65f6,y\u6700\u5927,\u5373x=15m\u65f6,\u82b1\u56ed\u9762\u79ef\u6700\u5927\uff0e
(1)AB=x,AD=1/2(40-AB)=20-x/2y=AB*AD=x(20-x/2)=-1/2x²+20x
因x>0,且AD<AB,所以
0<20-x/2<x,解这个不等式有40>x>40/3
(2)y=150,即
-1/2x²+20x-150=0,x²-40x+300=0
x1=30,x2=10(因不在x的取值范围内，故舍去)
AB=30m
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