1
vote
3answers
51 views

How do you solve two equal absolute value expressions?

I'm having trouble understanding how the following is solved. $$|x+1| = |x-2|$$
0
votes
3answers
80 views

Absolut value of cubic polynomial roots lower than 1

Assume we have a cubic polynomial $ x^3 +bx^2+xc+d=0 $, with b,c,d real numbers. Let $x_1, x_2, x_3 $ be the roots, either real or complex. What is the relation of the coefficients b,c and d in ...
1
vote
3answers
2k views

Proving square root of a square is the same as absolute value

Lets say I have a function defined as $f(x) = \sqrt {x^2}$. Common knowledge of square roots tells you to simplify to $f(x) = x$ (we'll call that $g(x)$) which may be the same problem, but it isn't ...
4
votes
2answers
213 views

Why isn't this square root $+$ or $-$?

I was tasked with proving the identity $\tan(\frac x 2) = \dfrac {\sin(x)}{1+\cos(x)}$ I used the quotient identity for tangent and the half angle identities for sine and cosine to get $ \pm \dfrac ...