\title{Upper-bound the square III}
\author{Gang Xiao}
\email{xiao@unice.fr}
\language{en}
\options{nofloat}
\methods{ineq/addterm, ineq/mulexp, ineq/exsides,
ineq/trans, ineq/constineq, ineq/addineq, ineq/mulineq,
ineq/sqrpos}
\minsteps{2}

\text{x=random(a,b,c,d,r,s,t,x,y,z)}
\integer{a=random(10..50)}
\integer{b=random(10..50)}
\integer{c=random(1..20)*random(-1,1)}
\integer{d=max(\a-(\c),\b+(\c))}
\integer{sqr=\d^2}

\function{fn=\x+\c}
\text{eqr=random(,=)}
\text{less=<\eqr}
\text{more=>\eqr}
\text{left=\x \more -\a}
\text{right=\x \less \b}
\context{\left
\right
}

\statement{Find the best upper bound for \((\fn)^2), when
<p><center>
\(-\a \less \x \less \b) .
</center>
}

\text{test=}
\text{cut=wims(translate internal <=> to , ; in \newobject)}
\if{; notin \cut and , isin \cut}{
 \text{left=item(1,\cut)}
 \text{right=item(2,\cut)}
 \text{test=yacas(Simplify((\fn)^2 - (\left)))}
}

\condition{\test issametext 0 and \right = \sqr}

