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 maximum value of the function f(x) = -x^2 + 5x - 8 in the interval [0, 10]?
+
Question: What is the derivative of f(x) = 3x^2 - 7x + 5 with respect to x?
+
What is the Pythagorean theorem, and how can it be used to find the length of the hypotenuse in a right-angled triangle?
+
New questions in Mathematics
1 + 1
2+2
Consider the relation R defined on the set of positive integers as (x,y) ∈ R if x divides y. Choose all the true statements. R is reflexive. R is symmetric. R is antisymmetric. R is transitive. R is a partial order. R is a total order. R is an equivalence relation.
STUDENTS IN A CLASS LEARN ONLY ONE FOREIGN LANGUAGE. two-sevenths of the students learn German, half of the students learn Spanish, and the remaining six students learn Italian. what is the number of students in this class? detail your reasoning carefully.
If L = (-2, -5) is reflected across y= -4 , what are the coordinates of L?
Express the following numbers in decimal system, where the subscript indicates the base: 110101 (SUBINDEX=2)
solve the following trigo equation for 0Β°<= x <= 360Β°. sec x =-2
224 Γ— (6Γ·8)
What is 28 marks out of 56 as a percentage
Three squares have a total area of 35.25 π‘π‘š2 . 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.
If a two-branch parallel current divider network, if the resistance of one branch is doubled while keeping all other factors constant, what happens to the current flow through that branch and the other branch? Select one: a. The current through the doubled resistance branch remains unchanged, and the current through the other branch decreases. b. The current through the doubled resistance branch decreases, and the current through the other branch remains unchanged. c. The current through the doubled resistance branch increases, and the current through the other branch remains unchanged. d. The current through both branches remain unchanged.
From 1975 through 2020 the mean annual gain of the Dow Jones Industrial Average was 652. A random sample of 34 years is selected from this population. What is the probability that the mean gain for the sample was between 400 and 800? Assume the standard deviation is 1539
Let x be an integer. Prove that x^2 is even if and only if is divisible by 4.
2x-5-x+2=5x-11
Find the equation of a straight line that has slope 3 and passes through the point of (1, 7) . Write the equation of the line in general forms
To paint a 250 m wall, a number of workers were employed. If the wall were 30 m longer, 9 more workers would be needed. How many were employed at the beginning?
t+72/t=-17
I have a complex function I would like to integrate over. I can use two approaches and they should give the same solution. If I want to find the contour integral βˆ«π›Ύπ‘§Β―π‘‘π‘§ for where 𝛾 is the circle |π‘§βˆ’π‘–|=3 oriented counterclockwise I get the following: ∫2πœ‹0𝑖+3π‘’π‘–π‘‘βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―π‘‘(𝑖+3𝑒𝑖𝑑)=∫2πœ‹03𝑖(βˆ’π‘–+3π‘’βˆ’π‘–π‘‘)𝑒𝑖𝑑𝑑𝑑=18πœ‹π‘– If I directly apply the Residue Theorem, I would get βˆ«π›Ύπ‘§Β―π‘‘π‘§=2πœ‹π‘–Res(𝑓,𝑧=0)=2πœ‹π‘–
Solve the system of equations by the addition method. 0.01x-0.08y=-0.1 0.2x+0.6y=0.2
In an experiment to assess the effect of listening to audiobooks while driving, participants were asked to drive down a straight road in a driving simulator. The accompanying data on time (in milliseconds) to react when a pedestrian walked into the street for 10 drivers listening to an audiobook are consistent with summary statistics and graphs that appeared in the paper "Good Distractions: Testing the Effect of Listening to an Audiobook on Driving Performance in Simple and Complex Road Environments."† (Round your answers to four decimal places.) 1,018 1,007 1,054 988 937 1,030 1,065 1,011 860 1,106 A button hyperlink to the SALT program that reads: Use SALT. Calculate the variance for this data set. 7437.7333 Incorrect: Your answer is incorrect. Calculate the standard deviation for this data set. 86.2022 Incorrect: Your answer is incorrect.

You might be interested in