document.write( "Question 899344: the sum of two irrational numbers multiplied by the larger one is 70 and their difference is multiplied by the smaller one is 12 \n" ); document.write( "

Algebra.Com's Answer #545320 by josgarithmetic(39618) $\"\"$ $\"About$

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Two numbers x and y, let $\"x%3Cy\"$ .
\n" ); document.write( " $\"%28sqrt%28x%29%2Bsqrt%28y%29%29sqrt%28y%29=70\"$ ----the first part of description
\n" ); document.write( " $\"sqrt%28xy%29%2By=70\"$
\n" ); document.write( " $\"sqrt%28xy%29=70-y\"$ \r
\n" ); document.write( "\n" ); document.write( "-
\n" ); document.write( " $\"%28sqrt%28y%29-sqrt%28x%29%29sqrt%28x%29=12\"$ ----the second part of description
\n" ); document.write( " $\"sqrt%28xy%29-x=12\"$
\n" ); document.write( " $\"sqrt%28xy%29=x%2B12\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Two formulas for sqrt(xy) must be equal.
\n" ); document.write( " $\"70-y=x%2B12\"$
\n" ); document.write( " $\"highlight_green%28x%2By=58%29\"$ AND $\"highlight_green%28x%3Cy%29\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "This seems to make possible many solutions for x and y to form irrational $\"sqrt%28x%29\"$ and $\"sqrt%28y%29\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "One example, but not the only example, should be $\"highlight%28x=28%29\"$ and $\"highlight%28y=30%29\"$ .
\n" ); document.write( "Their square roots are irrational.
\n" ); document.write( "I did NOT check these results.
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