MathMaster logo

MathMaster

  1. Home
  2. general
  3. prove that if n is a perfect square then n 2 is not perfect square
Question

Prove that if n is a perfect square,then n+2 is not perfect square

289

likes
1443 views

Answer to a math question Prove that if n is a perfect square,then n+2 is not perfect square

Expert avatar
Jett
4.7
97 Answers
Suppose n=a^2 and n+2=\:b^2 with a and b integers. Then b^2-a^2=2 which causes us to believe that bโˆ’a=1 and b+a=2 or even worse, b=1.5 โ€” Contradiction

Frequently asked questions (FAQs)
Question: How many ways can you arrange a group of 5 people out of 10?
+
Question: Factorize the expression 4x^2 + 12x - 16 using the distributive property.
+
What is the period of the trigonometric function f(x) = 3sin(4x) + 2cos(8x)?
+
New questions in Mathematics
Add. 7/wยฒ+18w+81 + 1/wยฒ-81
CASE 6-1: PREPARE A PRODUCTION PLAN: WHAT PROBLEMS ARRIVE? Midwest Plastics Company has conducted profit planning for several years. The president stated (with justification) that inventory control and planning had not been satisfactory, which was mainly due to poor planning of production and inventory budgets. Please analyze and provide recommendations, in detail, on the issue regarding the 20B profit plan, which is now being prepared. Their analysis and recommendations will be presented to the executive committee. Despite the seasonality factor, the sales department has been successful in developing a sales plan, on a monthly basis, for each year. The following sales data is available for 20B. 1. Sales plan summary for 20B: 2. Finished goods inventory, as of January 1, 20B, is 96,000 units. 3. Work-in-process inventory will remain constant. 4. Actual annual sales in 20A, including the estimate for December, were 350,000 units. 5. The average finished goods inventory during 20A was 70,000 units. IT IS REQUESTED. 1. Prepare the annual production budget, assuming that management policy is to budget ending finished goods inventory at a standard quantity, based on the ratio of historical sales of 20A to inventory turnover. 2. Prepare a schedule showing sales, production, and inventory levels for each month, assuming: 1) stable inventory, 2) stable production, and 3) recommended inventory-production levels. In developing your recommendations, assume that the following policies have been established: a) The president has set the policy that a maximum inventory of 85,000 units and a minimum inventory of 75,000 units should be used, except in abnormal circumstances. b) A stable level of production is definitely preferred, except that during the holiday season in July and August, production may be reduced by 25 percent. Likewise, a variation in production of 7.5 percent above and below the average level is acceptable. 3. What are the main problems faced by the company in production planning? Make your general recommendations.
The graph of the equation xยฒ= 4py is a parabola with focus F(_,_) and directrix y=_____ Therefore, the graph of xยฒ=12y is a parabola with focus F(_,_) and a directrix y=_____
The miles per gallon (mpg) for each of 20 medium-sized cars selected from a production line during the month of March are listed below. 23.0 21.2 23.5 23.6 20.1 24.3 25.2 26.9 24.6 22.6 26.1 23.1 25.8 24.6 24.3 24.1 24.8 22.1 22.8 24.5 (a) Find the z-scores for the largest measurement. (Round your answers to two decimal places.) z =
The average number of babies born at a hospital is 6 per hour. What is the probability that three babies are born during a particular 1 hour period?
Determine the reduced equation of the straight line that is perpendicular to the straight line r: y=4x-10 and passes through the origin of the Cartesian plane
Calculate the boiling temperature and freezing temperature at 1 atmosphere pressure of a solution formed by dissolving 123 grams of ferrous oxide in 1.890 grams of HCl.
Nice's central library building is considered one of the most original in the world, as it is a mix between a sculpture and a work of habitable architecture. It was called La Tรชte Carrรฉe and is made up of part of a bust that supports a cube divided into five floors. It is known that the building has a total height of approximately 30 meters. It admits that the cubic part of the sculpture is parallel to the floor and has a volume of 2744 meters3 Calculate, in meters, the height of the bust that supports the cube. Displays all the calculations you made.
It is known that the content of milk that is actually in a bag distributes normally with an average of 900 grams and variance 25 square grams. Suppose that the cost in pesos of a bag of milk is given by ๐ถ(๐‘ฅ) = { 3800 ๐‘ ๐‘– ๐‘ฅ โ‰ค 890 4500 ๐‘ ๐‘– ๐‘ฅ > 890 Find the expected cost.
Convert 9/13 to a percent
Xยณ-27
A function is considered exponential when it has a base with positive values greater than zero and different from one, where the exponent is an unknown. An important characteristic of exponential functions is that they show rapid growth or decay as an independent variable increases or decreases. Given the function 25^(x+3)=125, it is calculated that x has the value of
The grading on a $159,775 house comes to $3974.75. What percent of the total cost is this? (Express your answer to the nearest hundredth percent.)
48 kg of 30% sulfuric acid in a mixture of 10% and 40% sulfuric acid arose. How many kilograms were each of the original solutions?
The average weekly earnings in the leisure and hospitality industry group for a reโ€ cent year was $273. A random sample of 40 workers showed weekly average earโ€ nings of $285 with the population standard deviation equal to 58. At the 0.05 level of significance can it be concluded that the mean differs from $273? Find a 95% conโ€ fidence interval for the weekly earnings and show that it supports the results of the hypothesis test.
2 - 6x = -16x + 28
56 ร— 12 = 672. How should you adjust this answer 672 to determine 57 ร— 12? a) The answer increases by 1 b) The answer increases by 57 c) The answer increases by 56 d) The answer increases by 12
Kayla started a book club at her school. The number of girls in the book club was one more than twice the number of boys. If there are 15 girls in the book club, how many boys are in the club?
What is the set-off agreement? Make your own example, describe and put in T accounts how you record transactions.
g(x)=3(x+8). What is the value of g(12)

You might be interested in