MHB Why x2 +1 and x2 -1 are Not/Are Difference of Squares

  • Thread starter Thread starter Abdullah Qureshi
  • Start date Start date
  • Tags Tags
    Difference Squares
Abdullah Qureshi
Messages
16
Reaction score
0
Explain why x2 +1 is not a difference of squares and x2 -1 is
 
Mathematics news on Phys.org
Oh, but it is ...

$x^2+1 = x^2 - (-1) = (x - i)(x + i)$
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'Useless continued fraction for 1'

I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
View full post »

Similar threads

MHB Square metric not satisfying the SAS postulate
Replies
3
Views
4K
B Why is x2 . y2 not equal to (x-y) (x+y)?
Replies
1
Views
1K
I Understanding a quote about implicit differentiation
Replies
4
Views
1K
MHB Tell me, must I use m = (y2 - y1)/(x2 - x1), where m is 1/4?
Replies
12
Views
2K
MHB Intersection points of two quadratic functions
Replies
1
Views
2K
B Combinatorics and Magic squares
Replies
2
Views
2K
MHB Finding Squares in a Square Box: n > 1
Replies
1
Views
1K
I What does negative ratio mean in mathematics?
Replies
18
Views
19K
MHB Average rate of change in the function from x1 to x2
Replies
5
Views
3K
B Understanding why πr^2 works for different area calculations
Replies
7
Views
2K

Hot Threads

Recent Insights

Back
Top