Grade 7, Calculation of the whole test, 3 questions

1.Of the 2 55 3 44 4 4 33 5 22, which is the highest value? (To process).

Because 2 5 = 32, 3 4 = 81, 2 3 = 8, 5 2 = 25, 3 4>2 5>>5 2>2 3

So 3 44> 2 55 5 22>2 33 is the largest: 3 44

x 4 2000 - 8 100 x to process x [(5) 2003] 2 to process.

For any positive integer n, there is.

1/[(n+1)√n+n√(n+1)]

1/=(√(n+1)-√n)/

√(n+1)-√n)/

√(n+1)-√n)/[√n√(n+1)]=1/√n-1/√(n+1)

Original = 1-1 2+1 2-1 3+1 3-1 4+......1/√99-1/√100

x=(√5+1)/2

x^2=(3+√5)/2

1/x=2/(√5+1)=(√5-1)/21/x^2=(5+1-2√5)/4=(3-√5)/2(x^3+x+1)/x^4

x+1/x+1/x^2)/x^2

(√5+1)/2+(√5-1)/2+(3-√5)/2]=[(3+√5)/2]/x^2

x^2/x^2=1③

x^2-2√2x+2=-1+2

x-√2)^2=1

x-√2=±1

x = 2-1 or x = 2+1

x 2-2 2x+1=0 x 2+1=2 2xx+(1 x)=(x 2+1) x=2 2x x=2 2x-(1 x)= 2-1-[1 (2-1)]= 2-1- 2-1= -2 or.

x-(1/x)=√2+1-[1/(√2+1)]=√2+1-√2+1= 2

The first question can be denominated, using the square difference, and then dismantling them separately, and it can be seen that in the end, only the first term 1 and the last term are left with a negative hundredth of a root sign of 100.

Damn, it's so simple and ask. It looks like the second year of junior high school.

Is it so difficult to ask for a first-year junior high school question? Modern education is so powerful!

I'm so hard ... Do hair, ** the topic.

Students, is this really a simple arithmetic problem in the first year of junior high school? Are there any examples? If so, you can take a look at the examples! I can only answer the last two questions for you.

Let's talk about the third one first, it's relatively simple, first of all, do you know the Vedic theorem, you can use the Vedic theorem!

The second one, my algorithm is to divide the equation up and down by the fourth power of x, to get a formula, there is a value of x, calculate the value of one part of x, when you calculate this value, you can multiply the root number five minus one up and down, get a relatively simple formula, and then extract the common factor, there are also skills when extracting the common factor, first manage the last two formulas, that is, first extract the common factor of the last two formulas, by the way, the first formula to get is, one part of x plus one third of the third half of x plus one fourth of the fourth power of x!

I don't know if I can help you, haha, this question should be inferred, if there is an example question. It is recommended that you take a look at the example questions, which will be easier to understand, because these questions, especially in the first year of junior high school, require you to draw inferences!

Solution: This is a few quadratic radical operation problems, the writing is too complicated, so it is written in other software, and the solution process is shown in the figure.