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)

Question: What is the domain of the trigonometric function f(x) = sin(2x) + cos(x) + tan(x) - 1 in radians?

Question: Graph the inequality y > 2x - 1. Determine the solution region and shade it. Identify the x-values for which y > 2. How does the solution region change if the inequality is in the form y < 2x - 1 instead?

Math question: What is the second derivative of f(x) = 3x^4 - 6x^2 + 2x - 5 at x = 2?

New questions in Mathematics

-11+29-18

The derivative of a power is obtained just by subtracting 1 from the power True or false

1 plus 1

(3x^(2) 9x 6)/(5x^(2)-20)

If eight basketball teams participate in a tournament, find the number of different ways that first, second, and third places can be decided assuming that no ties are allowed.

calculate the area in square units of A rectangle with length 6cm and breadth 5cm

determine the polynomial F of degree 2 that interpolates. f at points (0;1) (2;5) (4;6). calculate F(0.8). Note: Using the polynomial expression with difference operator.

With the aim of identifying the presence of the feline leukemia virus (FeLV), blood samples were collected from cats sent to a private veterinary clinic in the city of Belo Horizonte. Among the animals treated, it was possible to observe that age followed a Normal distribution with a mean of 4.44 years and a standard deviation of 1.09 years. Considering this information, determine the value of the third quartile of the ages of the animals treated at this veterinary clinic. ATTENTION: Provide the answer to exactly FOUR decimal places

A box of numbered pens has 12 red, 12 blue, 12 green and 12 yellow pens. The pens for each colour are numbered from 1 to 12. There is a unique number on each pen, so no pen is exactly the same as any other pen in the box. When reaching into the box to randomly draw five pens without replacement, what is the proportion of getting exactly four pens of the same colour (Note: the numbers matter but the order does not)?

sum of 7a-4b+5c, -7a+4b-6c