algebraic surds and equations (1 Viewer)

[purpletree]

find all real x such that:

|4x-1|>2sqrt[x(1-x)]

 

[rolpsy]

 

[RealiseNothing]

Well x can't be negative otherwise that square root would be negative. So we can get rid of the absolute value brackets.



We can square it since we know x isn't negative:



Take everything to the right:



Solve:



Hence we get x = 1/10 or 1/2, and we see that the RHS will be 0 when x=1, so evidently 1 is a solution.

Thus and

Using domain:

 

[Shadowdude]

Question: How did you align your inequalities?

 

[rolpsy]

Question: How did you align your inequalities?

just use

\begin{align*}
blah &< 2blah\\
2blah &> blah\\
etc.
\end{align*}

when in latex
(the asterisks are to prevent auto-numbering)

 

[Shadowdude]

just use

\begin{align*}
blah &< 2blah\\
2blah &> blah\\
etc.
\end{align*}

when in latex
(the asterisks are to prevent auto-numbering)

you are a lifesaver