问题 解答题

有人说,任何含有字母的代数式的值,都随着字母取值的变化而变化;有人说未必如此,还举了一个例子,说:不论x,y,取任何有理数,多项式(x3+3x2y-2xy2+1)+(x3-4x2y+3xy2-10)+(-xy2+x2y-2x3+3)的值恒等于一个常数,你认为哪种意见正确?请加以说明。

答案

解:因为+3)

=x3+3x2y-2xy2+1+x3-4x2y+3xy2-10-xy2+x2y-2x3+3

=-6。

由此可知,这个多项式的值确实与x,y的取值无关,恒等于-6,可见,后一种意见是正确的,即含有字母的代数式的值,有时随字母取值的变化而变化,有时和字母的取值无关,即是一个常数。

选择题
单项选择题

Many years ago, when I was fresh out of school and working in Denver, I was driving to my parents’ home in Missouri for Christmas. I stopped at a gas station(加油站) about 50 miles from Oklahoma City, where I was planning to stop and visit a friend. While I was standing inline at the cash register, I said hello to an older couple who were also paying for gas.

I took off, but had gone only a few miles when black smoke poured from the back of my car. I stopped and wondered what I should do. A car pulled up behind me. It was the couple I had spoken to at the gas station. They said they would take me to my friend’s home. We chatted on the way into the city, and when I got out of the car, the husband gave me his business card.

I wrote him and his wife a thank-you note for helping me. Soon afterward, I received a Christmas present from them. Their note that came with it said that helping me had made their holidays meaningful.

Years later, I drove to a meeting in a nearby town in the morning. In late afternoon I returned to my car and found that I’d left the lights on all day, and the battery was dead. Then I noticed that the Friendly Ford dealership—a shop selling cars was right next door. I walked over and found two salesmen in the showroom.

"Just how friendly is Friendly Ford" I asked and explained my trouble. They quickly drove a pickup truck to my car and started it. They would accept no payment, so when I got home, I wrote them a note to say thanks. I received a letter back from one of the salesmen. No one had ever taken the time to write him and say thank you, and it meant a lot, he said.

"Thank you" are two powerful words. They’re easy to say and mean so much.

The author planned to stop () at Oklahoma City.

A.to visit a friend

B.to see his parents

C.to pay at the cash register

D.to have more gas for his car