Question

(a-b)^2=(b-a)^2 where a and b are real numbers
is the statement ever correct?

Answer 1

yes

Answer 2

another way, a little wierd

\(\large\color{black}{ \displaystyle (a-b)^2=(b-a)^2 }\)

\(\large\color{black}{ \displaystyle \sqrt{ (a-b)^2}=\sqrt{(b-a)^2} }\)

\(\large\color{black}{ \displaystyle |a-b|=|b-a| }\)

Answer 3

or you know that let

a - b = C
and so
b - a = -C

you know (-C)^2=(C)^2

Answer 4

cool thanks

Answer 5

yes, the first approach is like a distance from "a" to "b"
and the second is noticing that \(\large\color{black}{ \displaystyle x^2=a^2 }\) then \(\large\color{black}{ \displaystyle x=\pm a }\)

Answer 6

you welcome, but remember this
that the definition of the absolute value of f(x) is

\(\large\color{black}{ \displaystyle |f(x)|=\sqrt{ \left[f(x){\color{white}{\LARGE|}}\right] ^2} }\)

Answer 7

for example, when you take a derivative of an absolute value, this is very helpful.