设x＞1，y＞1，且2logxy-2logyx+3=0，求T=x2-4y2的最小值．
令t=logxy，∵x＞1，y＞1，∴t＞0．
由2logxy-2logyx+3=0得2t-
+3=0，∴2t2+3t-2=0，2 t
∴（2t-1）（t+2）=0，∵t＞0，
∴t=
，即logxy=1 2
，∴y=x1 2
，1 2
∴T=x2-4y2=x2-4x=（x-2）2-4，
∵x＞1，
∴当x=2时，Tmin=-4．
| Computer programmer David Jones earns ￡35,000 a year designing new computer games, yet he cannot find a bank prepared to let him have a check card. Instead, he has been told to wait another two years, until he is 18. The 16-year-old works for a small firm in Liverpool, where the problem of most young people of his age is finding a job. David’s firm releases two new games for the expanding home computer market each month. But David’s biggest headache is what to do with his money. Despite his salary, earned by inventing new programs within fight schedules, with bonus payments and profit-sharing, he cannot drive a car, take out a mortgage, or obtain credit cards. He lives with his parents in their council house in Liverpool, where his father is a bus driver. His company has to pay ￡150 a month in taxi fares to get him the five miles to work and back every day because David cannot drive. David got his job with the Liverpool-based company four months ago, a year after leaving school with six O-levels and working for a time in a computer shop. "I got the job because the people who run the firm knew I had already written some programs," he said. "I suppose ￡35,000 sounds a lot but actually that’s being pessimistic. I hope it will come to more than that this year." He spends some of his money on records and clothes, and gives his mother ￡20 a week. But most of his spare time is spent working. "Unfortunately, computing was not part of our studies at school," he said. "But I had been studying it in books and magazines for four years in my spare time. I knew what I wanted to do and never considered staying on at school. Most people in this business are fairly young, anyway." David added, "I would like to earn a million and I suppose early retirement is a possibility. You never know when the market might disappear." |
Why is David different from other young people of his age
A．He earns an extremely high salary.
B．He is employed.
C．He does not go out much.
D．He lives at home with his parents.