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 b−a=1 and b+a=2 or even worse, b=1.5 — Contradiction

Frequently asked questions (FAQs)
What is 3/4 in decimal form?
+
What is the value of f(g(2)) if f(x) = 3x + 5 and g(x) = 2x - 1?
+
Math Question: Graph the inequality 2x + 4y ≥ 8 on a coordinate plane. (
+
New questions in Mathematics
a to the power of 2 minus 16 over a plus 4, what is the result?
5 squirrels were found to have an average weight of 9.3 ounces with a sample standard deviation is 1.1. Find the 95% confidence interval of the true mean weight
³√12 x ⁶√96
(2b) to the 1/4th power. Write the expression in radical form.
-0.15/32.6
How long will it take for $900 to become $5000 at an annual rate of 11.15% compounded bimonthly?
A construction company is working on two projects: house construction and building construction. Each house requires 4 weeks of work and produces a profit of $50,000. Each building requires 8 weeks of work and produces a profit of $100,000. The company has a total of 24 work weeks available. Furthermore, it is known that at least 2 houses and at least 1 building must be built to meet the demand. The company wants to maximize its profits and needs to determine how many houses and buildings it should build to meet demand and maximize profits, given time and demand constraints.
How many anagrams of the word STROMEC there that do not contain STROM, MOST, MOC or CEST as a subword? By subword is meant anything that is created by omitting some letters - for example, the word EMROSCT contains both MOC and MOST as subwords.
Three squares have a total area of 35.25 𝑐𝑚2 . The larger square has twice the side-length of the middle-sized square. The smaller square has its side length exactly 0.5 cm smaller than the middle-sixed square. Find the side lengths of each of the three squares.
7. Find the equation of the line passing through the points (−4,−2) 𝑎𝑛𝑑 (3,6), give the equation in the form 𝑎𝑥+𝑏𝑦+𝑐=0, where 𝑎,𝑏,𝑐 are whole numbers and 𝑎>0.
A warehouse employs 23 workers on first​ shift, 19 workers on second​ shift, and 12 workers on third shift. Eight workers are chosen at random to be interviewed about the work environment. Find the probability of choosing exactly five first ​-shift workers.
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: • How many hectares of each crop must be allocated so that the profit is maximum. R= • The estimated profits for the ejidal cooperative in the next growing season. R=
Let A, B, C and D be sets such that | A| = |C| and |B| = |D|. Prove that |A × B| = |C × D|
How to do 15 x 3304
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 ̄<10hours HA : x ̄ > 13.5 hours
effectiveness of fiscal and monetary policy under closed and open economies
If the mean of the following numbers is 17, find the c value. Produce an algebraic solution. Guess and check is unacceptable. 12, 18, 21, c, 13
y′ = 2x + 3y x′ = 7x − 4y x(0) = 2 y(0) = −1 sisteminin ¸c¨oz¨um¨un¨u bulunuz. (Lineer Denk. Sis.)
Recall that with base- ten blocks, 1 long = 10 units, 1flat = 10 long, and a block = 1 unit. Then what number does 5 flat, 17long and 5 units represent represent ?
A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 55.0 min at 100.0 km/h, 14.0 min at 65.0 km/h, and 45.0 min at 60.0 km/h and spends 20.0 min eating lunch and buying gas. (a) Determine the average speed for the trip.

You might be interested in