问题 解答题

根据下列问题,列出关于x的方程,并将其化成一元二次方程的一般形式.

(1)4个完全相同的正方形的面积之和是25,求正方形的边长x.

(2)一个矩形的长比宽多2,面积是100,求矩形的长x.

(3)一个直角三角形的斜边长为10,两条直角边相差2,求较长的直角边长x.

答案

(1)依题意得,4x2=25,

化为一元二次方程的一般形式得,4x2-25=0.

(2)依题意得,x(x-2)=100,

化为一元二次方程的一般形式得,x2-2x-100=0.

(3)依题意得,x2+(x-2)2=102

化为一元二次方程的一般形式得,x2-2x-48=0.

阅读理解

阅读理解。

       After a serious earthquake happened, a father left his wife safely at home and rushed to his son's

  school, only to find that the building where his son studied had collapsed and looked like a pancake.

       He was shocked. He didn't know what he should do for a while, then he remembered the words he

  had said to his son, "No matter what happens, I'll always be there for you! "And tears began to fill his

  eyes. He started digging through the ruins (废墟).

       As he was digging, other helpless parents and the firemen arrived and tried to pull him off the ruins,

  saying, "It's too late! They're all dead! There's nothing you can do! " To them he replied with one line,

  "Are you going to help me now? " And then he kept on digging.

       No one helped, however. He went on alone because he needed to know for himself: "Is my boy alive

  or is he dead? " He dug for eight hours. . . 12 hours. . . 24 hours. . . 36 hours. . . then, in the 39th hour,

  he pulled back a rock and heard his son's words. He shouted his son's name, "ARMAND! " He heard

  back, "Dad! It's me, Dad! I told the other kids not to worry. I told them that if you were alive, you'd save

   me and when you saved me, they'd be saved. You promised, 'No matter what happens, I'll always be

  there for you! You did it, Dad! "

       "What's going on in there? How is it? " the father asked.

       "There are 14 of us left out of 33, Dad. We're frightened, hungry, thirsty and thankful you're here.

  When the building fell down, it made a triangle (三角) , and it saved us."

       "Come out, boy!"

       "No, Dad! Let the other kids out first, because I know you'll get me! No matter what happens, I

  know you'll always be there for me!"

1. The underlined word "collapsed" probably means "_____".

A. break down    

B. shake away      

C. stand by          

D. fall into

2. Who came to help the father when he was digging?

A. His wife.      

B. Other parents.  

C. The firemen.      

D. No one.

3. Other parents and the firemen wanted to pull him off the ruins because they thought _____.

A. he was mad

B. all the children had died in the earthquake

C. he was too dangerous to others

D. it was not his job to dig

4. How many students were already dead when the father found them in the ruins?

A. Fourteen.      

B. Thirty-three.    

C. Forty-seven.      

D. Nineteen.

5. We can learn from the passage that _____.

A. it took the father one day to find his son and other students

B. his wife died in the earthquake

C. his son was the last one to come out of the ruins

D. the son didn't believe his father would come to save him

多项选择题