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 bβˆ’a=1 and b+a=2 or even worse, b=1.5 β€” Contradiction

Frequently asked questions (FAQs)
What is the integral of cos(x)
+
What are the unit vector components of a vector with magnitude |v| = 5 and angle ΞΈ = 60Β°?
+
What is the minimum number of vertices a graph can have if its basic shape is a straight line?
+
New questions in Mathematics
Using a remarkable product you must factor the expression: f(x) =36x^2-324 and you are entitled to 5 steps
Let f(x)=||x|βˆ’6|+|15βˆ’|x|| . Then f(6)+f(15) is equal to:
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 random variable Y is defined as the sum between two different integers selected at random between -4 and 2 (both included). What are the possible values of the random variable Y? What is the value of P(Y=-3)? And whether it is less than or equal to -5?
Determine the equations of the lines that pass through the following points P1 (2;-1) and p2 (4;-1)
Let I βŠ‚ R be a bounded and nonempty interval. Show that there are numbers a, b ∈ R with a ≀ b and I =[a,b] or I =[a,b) or I =(a,b] or I =(a,b)
Reparameterize the curve r(t)= cos(t)i without (t)j (t)k by the arc length.
In a grocery store, when you take out 3 peppers and 4 carrots, there are 26 peppers and 46 carrots left. How many peppers and carrots were there initially?
The cost of unleaded gasoline in the Bay Area once followed an unknown distribution with a mean of $4.59 and a standard deviation of $0.10. Sixteen gas stations from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the 16 gas stations. 84. Find the probability that the average price for 30 gas stations is less than $4.55. a 0.6554 b 0.3446 c 0.0142 d 0.9858 e 0
Two business partners have a bank balance of $17,942.00. After the first year their interest brings their balance to $18,928.91. What rate of interest is earned?
The price per night of a suite at the Baglioni Hotel in Venice is 1896 euros, VAT included. The VAT in Italy is 25%. The hotel gets a return of 10% out of the price VAT included. b) What is the profit value made by the hotel for one
Exercise 1 An ejidal association wishes to determine the distribution for the three different crops that it can plant for the next season on its available 900 hectares. Information on the total available and how many resources are required for each hectare of cultivation is shown in the following tables: Total available resource Water 15,000 m3 Fertilizer 5,000 kg Labor 125 day laborers Requirements per cultivated hectare Corn Soybeans Wheat Water 15 25 20 Fertilizer 5 8 7 Labor** 1/8 1/5 1/4 *The data in fraction means that with one day laborer it will be possible to care for 8, 5 and 4 hectares respectively. * Sales of crops 1 and 3, according to information from the Department of Agriculture, are guaranteed and exceed the capacity of the cooperative. However, soybeans must be limited to a maximum of 150 hectares. On the other hand, the profits for each hectare of crop obtained are estimated at: $7,500 for corn, $8,500 for soybeans and $8,000 for wheat. The objectives are to determine: β€’ How many hectares of each crop must be allocated so that the profit is maximum. R= β€’ The estimated profits for the ejidal cooperative in the next growing season. R=
Solve the following equation for x in exact form and then find the value to the nearest hundredths (make sure to show your work): 5e3x – 3 = 25
If a|-7 and a|9, then a|-63
7.57 Online communication. A study suggests that the average college student spends 10 hours per week communicating with others online. You believe that this is an underestimate and decide to collect your own sample for a hypothesis test. You randomly sample 60 students from your dorm and find that on average they spent 13.5 hours a week communicating with others online. A friend of yours, who offers to help you with the hypothesis test, comes up with the following set of hypotheses. Indicate any errors you see. H0 :x Μ„<10hours HA : x Μ„ > 13.5 hours
Build a truth table for the statement ~(pvq)^~p
17. A loan for $104259 is taken out for 10 years with an annual interest rate of 9.4%, compounded quarterly. What quarterly payment is required to pay the loan off in 10 years? Enter to the nearest cent (two decimals). Do not use $ signs or commas in the answer.
15.A newly married couple purchased a home with a $123710 down payment. They financed the remaining balance of the home with a mortgage. Their payments were $15395 at the end of every six months for 23 years and the interest rate was 10.6%, compounded semi-annually. How much did they purchase their home for. Enter to the nearest cent (two decimals). Do not use $ signs or commas in the answer.
X^3 - x^2 - 4 = 0, what are the values of x?
Sarah is lining a square tray with 1 inch square tiles. the side length of the tray is 9 inches. How many tiles does Sarah need?

You might be interested in