Question 899344
Two numbers x and y, let {{{x<y}}}.
{{{(sqrt(x)+sqrt(y))sqrt(y)=70}}}----the first part of description
{{{sqrt(xy)+y=70}}}
{{{sqrt(xy)=70-y}}}

-
{{{(sqrt(y)-sqrt(x))sqrt(x)=12}}}----the second part of description
{{{sqrt(xy)-x=12}}}
{{{sqrt(xy)=x+12}}}


Two formulas for sqrt(xy) must be equal.
{{{70-y=x+12}}}
{{{highlight_green(x+y=58)}}} AND {{{highlight_green(x<y)}}}.


This seems to make possible many solutions for x and y to form irrational {{{sqrt(x)}}} and {{{sqrt(y)}}}.


One example, but not the only example, should be {{{highlight(x=28)}}} and {{{highlight(y=30)}}}.
Their square roots are irrational.
I did NOT check these results.