We know that x is an integer, and the sum of X-2 / 3 plus 2 / 3 plus the square of x minus 2x + 18 / 9 is an integer

We know that x is an integer, and the sum of X-2 / 3 plus 2 / 3 plus the square of x minus 2x + 18 / 9 is an integer

The square of X is an integer. There is no doubt that the square of X is an integer. If 2x + 18 of 9 wants to be an integer, 2x + 18 must be a multiple of 9, or 2x is a multiple of 9. Let 2x = 9y, y be an integer, x = 9 / 2Y

Known (x's square + Y's Square) × (x's square + Y's square + 2) minus 8 = 0, find the value of X's square + Y's Square. Find the specific process. Depend on you!

Let t = the square of X + the square of Y
Then (square of X + square of Y) × (square of X + square of Y + 2) minus 8 = 0
That is t (T + 2) - 8 = 0
t²+2t-8=0
The solution is t = - 4 (rounding off) or T = 2
Square of X + square of y = 2

The square of x minus the square of y plus 2 times y minus 1

x²-y²+2y-1
=x²-(y²-2y+1)
=x²-(y-1)²
=[x+(y-1)][x-(y-1)]
=(x+y-1)(x-y+1)

A worker originally planned to produce a batch of parts in 13 hours. Later, because he produced 10 more parts per hour, he not only completed the task in 12 hours, but also produced 60 more parts than the original plan. How many parts did he plan to produce?

Suppose the original plan produces x parts, according to the meaning of the question: x + 6012-x13 = 10, solving the equation: x = 780. Answer: the original plan produces 780 parts

If a worker processes a batch of parts in the planned time, if he does 35 parts per hour, he will lose 10 and can't complete the task. If he does 40 parts per hour, he will overfulfil 20. Ask him how many parts he needs to process? What is the specified time? (solve the equation)!

Total amount - 35 * (working hours) = 10
40 * (working hours) - 20 = total
Working hours = 6
Total = 220

Processing a batch of parts, the original plan to complete 15 days, the actual daily processing of 30, only 10 days to complete the task, how many of these parts?

A: there are 900 parts in this batch

A factory produces a batch of parts, which was originally planned to be completed in 30 days, but actually completed in 20 days. In fact, there are 6 more machines per day than the original plan. How many machines are there?

The original plan is to produce X machines per day
30X=20(X+6）
X = 12 (set)
30x = 30 * 12 = 360 (set)
The answer is 360

Someone undertakes to make a batch of parts. He originally planned to make 40 parts a day, but he can complete the task on time. Due to the improvement of the process, the work efficiency has been increased by 20%. As a result, he not only finished 16 days ahead of schedule, but also overfulfilled 32 pieces. How many days are he expected to finish? How many parts were originally planned?

If the original schedule is x days and Y parts are customized, then 40x = y (1 + 20%) × 40 × (x − 16) = y + 32 and the solution is x = 100y = 4000

4. To produce a batch of parts, after finishing 2 / 3 of the task, the process was reformed, the daily working time was reduced by 1 / 4 compared with the plan, and the working efficiency was improved by 1 / 9
4. After a batch of parts were produced and two-thirds of the task was completed, the process was reformed. The daily working time was 1 / 4 less than the plan, and the work efficiency was improved by 1 / 9. As a result, it took 32 days to complete the task. How many days do you plan to complete the task?

32/[2/3+1/3/(1-1/4)/(1+1/9)]=30

The original plan was to process 30 parts per day. When 1 / 3 of the parts were processed, the work efficiency increased by 10% due to improved technology. As a result, the task was completed four days ahead of schedule?

1-13 = 23, 23 ^ (1 + 10%) = 2033, 4 ^ (23 − 2033) = 66 (days), 66 × 30 = 1980 (pieces); answer: this batch of parts has a total of 1980