document.write( "Question 1208932: I would like to see the prove for these two questions. \r
\n" ); document.write( "\n" ); document.write( "1. If a > 0, show that the solution set of the inequality x^2 < a consists of all numbers x for which -sqrt{a} < x < sqrt{a}.\r
\n" ); document.write( "\n" ); document.write( "2. If a > 0, show that the solution set of the inequality x^2 > a consists of all numbers x for which x < -sqrt{a} or x > sqrt{a}.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #847465 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "\r\n" );
document.write( "1. If , show that the solution set of the inequality  consists of all numbers x for which .\r\n" );
document.write( "\r\n" );
document.write( "Let us assume for contradiction that there exists x such that\r\n" );
document.write( "\r\n" );
document.write( ", yet \r\n" );
document.write( "\r\n" );
document.write( "Since , x is negative for it is less than a negative number.\r\n" );
document.write( "Then -x is a positive number and \r\n" );
document.write( "\r\n" );
document.write( " [both sides are positive]. Therefore,\r\n" );
document.write( " which contradicts .\r\n" );
document.write( "\r\n" );
document.write( "That's half the proof.\r\n" );
document.write( "\r\n" );
document.write( "Now assume for contradiction that there exists x such that\r\n" );
document.write( "\r\n" );
document.write( " such that , yet \r\n" );
document.write( "\r\n" );
document.write( "Since ,  which contradicts  \r\n" );
document.write( "\r\n" );
document.write( "Thus the proof is done, and \r\n" );
document.write( " \r\n" );
document.write( ",  implies .\r\n" );
document.write( "\r\n" );
document.write( "------------------\r\n" );
document.write( "2. If , show that the solution set of the inequality \r\n" );
document.write( "consists of all numbers x for which  or .\r\n" );
document.write( "\r\n" );
document.write( "Assume for contradiction that there exists x such that\r\n" );
document.write( "\r\n" );
document.write( " and , yet  \r\n" );
document.write( "\r\n" );
document.write( "Then both  and x are negative numbers, and thus -x is a \r\n" );
document.write( "positive number.\r\n" );
document.write( "\r\n" );
document.write( " implies  thus \r\n" );
document.write( "\r\n" );
document.write( "which contradicts \r\n" );
document.write( "\r\n" );
document.write( "That's half the proof. \r\n" );
document.write( "\r\n" );
document.write( "Next, assume for contradiction that there exists x such that\r\n" );
document.write( "\r\n" );
document.write( " and , yet  \r\n" );
document.write( "\r\n" );
document.write( "Then  implies  which contradicts .\r\n" );
document.write( "\r\n" );
document.write( "Then ,  implies \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );