Olympiad Mathematics, the process is clear and extra points, why don t Olympiad Mathematics add poin

Now Xiaojun is a year old and grandpa is 7a years old.

a+x=6(a+x) a=5x

a+y=5(a+y) a=2x

a+z=4(a+z) a=z

a+m=3(a+m) a=m/2

a+n=2(a+n) a=n/5

Since a is a positive integer, we can see from the first 1 and 2 that a must be a common multiple of 2 and 5.

From 3, 4, 5, we can see that z m n is 1 times, 2 times and 5 times of a, respectively.

Therefore, a can be a minimum value of 10

At this time, x=2 y=5 z=10 m=20 n=50, so grandpa is now 70 years old and Xiaojun is 10 years old.

2 years later, Grandpa 72 Xiaojun 12 Grandpa is 6 times that of Xiaojun.

After 5 years, Grandpa 75 Xiaojun 15 Grandpa is 5 times that of Xiaojun.

10 years later, Grandpa 80 Xiaojun 20 Grandpa is 4 times that of Xiaojun.

20 years later, Grandpa 90 Xiaojun 30 Grandpa is 3 times that of Xiaojun.

50 years later, Grandpa 120 Xiaojun 60 Grandpa is 2 times that of Xiaojun.

The difference is X years.

7 times more than you = 6 times more than you.

then x is a common multiple of . x = 60 years old.

6 times more = 60, 1 times = 10, so Xiaojun is 10 years old and grandpa is 70 years old; 70 10 = 7, grandpa is 7 times that of Xiaojun.

5 times = 60, 1 times = 12, Xiaojun is 12 years old, grandpa is 72 years old; 72 12 = 64 times = 60, 1 times = 15, Xiaojun is 15 years old, grandpa is 75 years old; 75 15 = 53 times = 60, 1 times = 20, Xiaojun is 20 years old, grandpa is 80 years old; 80 20 = 42 times = 60, 1 times = 30, Xiaojun is 30 years old, grandpa is 90 years old; 90 30 = 31 times = 60, Xiaojun is 60 years old, grandpa is 120 years old;

Arcane itself is mainly bai is not harmful, du is generally suitable for 2%-5% of gifted people to learn, and dao is now in the middle and high school entrance examinations because of the Olympiad awards and students to implement the answer bonus policy, parents in order to let their children add points and force their children to learn Olympiad is the main harm, some primary and secondary schools under the strict investigation of relevant departments, is still opening Olympiad classes for various reasons, some parents ignore their children's interests to force their children to learn Olympiad, and if they don't learn well, they will be beaten and scolded, This shows the severity of the situation.

I think the main source of harm is still the problem of China's education system, the concept that you can't go to university and don't have any chance of surviving, so only China has a headache for this, parents in order to cater to this concept, let their children die, the original talent has no positive effect on the society, and even finally become withdrawn, not tolerated by the society, and so on and so on we were not willing to see.

"Does my child want to learn the Olympiad?" When can I sign up for an Olympiad class? Fan Jianguo, a mathematics teacher and vice principal of Confucius Temple Primary School, has often been asked this question by parents of first-grade children who have just entered the school recently.

In the past, the two most well-known competitions in the field of primary school mathematics in our province, "Hua Cup" and "Decimal News", have been suspended for more than two years, and the bonus point policy for the high school entrance examination competition has been canceled since last year.

Principal Fan said that the first grade children learn the Olympiad, isn't it a joke? Yet so many parents are asking the same question.

It shows that the Olympiad is indeed "deeply rooted in the hearts of the people", and it is also worrying. The reporter learned that at present, there is no large-scale Olympiad competition in our province, only the "internal competition" launched by some tutoring classes of social schools, but all the "business opportunities" about the Olympiad in the society are not cold but prosperous. In a large comprehensive bookstore, the reporter roughly counted, there are more than 100 kinds of Olympiad books about various primary schools, and various social tutoring classes have also used the Olympiad as a signboard, generally from the third grade of primary school can be registered, many Olympiad classes also have their own competitions, and some even use the method of rolling elimination, that is, after the exam, they will be promoted to a level, otherwise they will continue to go, so that the child feels very stressed.

Some primary schools and even kindergartens have extracurricular math interest classes, but in fact, the so-called "interest" is mainly focused on Olympiad mathematics. The Olympiad fever has a tendency to "start from the baby".

Principal Fan analyzed that there are four main reasons for the continued popularity of the Olympiad: first, when the junior high school is promoted, the famous school attaches great importance to the results of the Olympiad, because the examination is cancelled at the junior high school, the selection of students mainly depends on the quality education report card and various awards, if the Olympiad can take advantage of the advantage, there is undoubtedly an extra weight; Second, some socially run tutorial classes take the opportunity to hype, so that parents do not know; In fact, most parents do not know about the Olympiad, and they don't care whether their children are interested in the Olympiad, but when they communicate, they found that their children have taken the Olympiad class, for fear that their children will miss it, so they blindly follow the trend and send their children to the Olympiad class; Fourth, parents' expectations for their children are too high, and they always hope that their children can learn more things and add more weight to future competition. In fact, Olympiad fever, especially in primary school, is very detrimental to children's development.

Measured by the curriculum standards, the Olympiad questions are biased, difficult, and strange, which seriously violates the spirit of the curriculum reform, and many of the content is actually the content that has been deleted from the curriculum reform many times since the founding of the People's Republic of China, and has no practical benefit to children's learning mathematics. Some seemingly mysterious problems actually have fixed formulas, as long as you memorize the formulas, you can solve them. For children with strong learning ability, spare energy, and interest in mathematics, it may be helpful to learn some Olympiad mathematics, but for most children, it is not only useless, but also mistaken children, because letting children drill those difficult problems that even adults find difficult, will make children always in the psychology of failure, and in the long run, the enthusiasm for learning will be seriously frustrated.

, apparently a≠-1

So (a+1)(a 2-a+1)=0

There is a 3+1=0, i.e. a 3=-1

a^2010=(a^3)^670=1

So a 2010+1 a 2010=1+1 1=2

2. (a^2+b^2)^3=(a^3+b^3)^3+8a^3*b^3

a^6+3a^2b^4+3a^4b^2+b^6=a^6+2a^3b^3+b^6+8a^3*b^3

There are 3a 2b 4+3a 4b 2=10a 3*b 3

i.e. 3(a2+b2)=10ab

Divide both sides by ab, and there is a b+b a=10 3

3.Let 2007x 2=2008y2=2009z2=2010w2=t2

1/x=(√2007)/t

1/y=(√2008)/t

1/z=(√2009)/t

1/w=(√2010)/t

The sum of these 4 equations has ( 2007 + 2008 + 2009 + 2010) t=1

i.e. t=(2007+ 2008+ 2009+ 2010).

At the same time, there is. 2007x=t*√2007

2008y=t*√2008

2009z=t*√2009

2010w=t*√2010

The sum of these 4 equations is 2007x+2008y+2009z+2010w=t*( 2007+ 2008+ 2009+ 2010)=t 2

So (2007x+2008y+2009z+2010w)= t 2=t=(2007+ 2008+ 2009+ 2010).

Solution: 1

a^2-a+1=0

a+1/a=1

a^2010+1/a^2010

a^2009+1/a^2009)(a+1/a)-a^2008-1/a^2008

a^2009+1/a^2009-a^2008-1/a^2008

a^2008+1/a^2008)(a+1/a)-a^2008-1/a^2008-a^2007-1/a^2007

(a^2007+1/a^2007)

(a^2006+1/a^2006)(a+1/a)+a^2005+1/a^2005

(a^2005+1/a^2005)(a+1/a)+a^2004+1/a^2004+a^2005+1/a^2005

a^2004+1/a^2004

…Rule: Each step of derivation can reduce the exponent by 3 and change the sign at the same time. The exponent is positive when it is even, and negative when the exponent is odd.

a^2010+1/a^2010

(a^3+1/a^3)

(a+1/a)(a^2-1+1/a^2)

[(a+1/a)^2-3]

2 Incidentally: This problem was solved incorrectly, and it was verified with A 6 + 1 A 6 to know that he was not solved correctly.

2、(a^2+b^2)^3=(a^3+b^3)^2+8a^3b^3

a^6+3a^4b^2+3a^2b^4+b^6=a^6+10a^3b^3+b^6

3a^4b^2+3a^2b^4=10a^3b^3

3(a/b)+3(b/a)=10

a/b)+(b/a)=10/3

3. Let 2007x 2=2008y 2=2009z 2=2010w 2=t

then x= (t 2007) y= (t 2008) z= (t 2009) w= (t 2010).

1/x+1/y+1/z+1/w=1

2007+√2008+√2009+√2010)/√t=1

t=√2007+√2008+√2009+√2010

2007x+2008y+2009z+2010w)

[√2007t)+√2008t)+√2009t)+√2010t)]

[√t(√2007+√2008+√2009+√2010)]

There is no solution to this question.

2. a^6+3a^4*b^2+3a^2*b^4+b^6=a^6+2a^3*b^3+b^6+8a^3*b^3

Vested 3a 4*b 2+3a 2*b 4=10a 3*b 3, both sides divided by a 3*b 3

3a b + 3b a = 10, i.e. b a + a b = 10 3

3.Let m=2007x 2=2008y=2009z2=2010w2, then x= (m 2007) y= (m 2008) z= (m 2009) w= (m 2010).

1/x+1/y+1/z+1/w=1

2007+√2008+√2009+√2010)/√m=1

t=√2007+√2008+√2009+√2010

2007x+2008y+2009z+2010w)

[√2007m)+√2008m)+√2009m)+√2010m)]

[√m(√2007+√2008+√2009+√2010)]

Happy New Year.

1.The answer is 1

A +1=a,a 2010+1 a 2010=[(a 2010) 2+1] (a 2010).

Let a 2010=x, the original formula = (x 2+1) x=x x=1

2.The answer is 8 3

The original title reads (a +b) (a +b) (a +b) = (a +b) (a +b )+8a b

Divide both sides by a, (1+ b a) (a+b a)(a +b ) = (1+ b a) (a +b )+8b

Divide both sides by b to get (1+ b a) (a b + b a) (a b +1) = (1+ b a) (a b +1) + 8

So, (a b + b a) = 8 3

3.The answer is 2007+ 2008+ 2009+ 2010

2007x²=2008y²=2009z²=2010w²

2007 x=√2008 y=√2009 z=√2010 w

y=√2007/√2008 x , z=√2007/√2009 x, w=√2007/√2010 x

1 x+1 y+1 z+1 w=1

Yes: 1 x + 1 (2007-2008 x) + 1 (2007-2009 x) + 1 (2007-2010 x) = 1

x=(√2007+√2008+√2009+√2010)/√2007

y=(√2007+√2008+√2009+√2010)/√2008

z=(√2007+√2008+√2009+√2010)/√2009

w=(√2007+√2008+√2009+√2010)/√2010

Root number 2007x+2008y+2009z+2010w = 2007+ 2008+ 2009+ 2010