\title{Sum and product II}
\author{Gang Xiao}
\email{xiao@unice.fr}
\language{en}
\options{nofloat}
\methods{ineq/rewrite, ineq/simpdeduc, ineq/lincomb,
ineq/mulnum, ineq/divnum, ineq/addineq, ineq/mulineq,
ineq/sqrpos}
\minsteps{4}

\matrix{vars=a,b
c,d
r,s
s,t
u,v
x,y
}
\text{vars=randomrow(\vars)}
\text{x=item(1,\vars)}
\text{y=item(2,\vars)}
\text{kind=random(rational numbers, real numbers)}

\text{cs=shuffle(25)}
\integer{c1=item(1,\cs)+2}
\integer{c2=item(2,\cs)+2}
\integer{n=random(50..100)*2}
\rational{s=\n^2/(4*\c1*\c2)}

\text{less=random(<,<=)}
\function{sum=\c1*\x + \c2*\y}
\text{ltn=\sum \less \n}

\context{\x > 0
\y > 0
\ltn
}
\text{prv=\x*\y \less \s}
\goal{\prv}

\statement{Let \(\x) and \(\y) be two positive \kind such that
\(\ltn). Prove
<p><center>
	\( \prv ) .
</center>
}

