document.write( "Question 446023: Solve:\r
\n" ); document.write( "\n" ); document.write( "(x^2 - 1)^1/2 + (x^2 - 1)^-1/2 = 2\r
\n" ); document.write( "\n" ); document.write( "Any help would be very much appreciated.\r
\n" ); document.write( "\n" ); document.write( "Thank you \n" ); document.write( "

Algebra.Com's Answer #307141 by Gogonati(855) $\"\"$ $\"About$

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$\"%28x%5E2-1%29%5E%281%2F2%29%2B1%2F%28x%5E2-1%29%5E%281%2F2%29=5%2F2\"$ ,multiply both sides by $\"%28x%5E2-1%29%5E%281%2F2%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2-1%29%2B1=%285%2F2%29%28x%5E2-1%29%5E%281%2F2%29\"$ => $\"x%5E2=%285%2F2%29%28x%5E2-1%29%5E%281%2F2%29\"$ . Raise to the\r
\n" ); document.write( "\n" ); document.write( "second power both sides of equation: $\"x%5E4=%2825%2F4%29%28x%5E2-1%29\"$ , set the equation to \r
\n" ); document.write( "\n" ); document.write( "zero: $\"4x%5E4-25x%5E2%2B25=0\"$ , substitute $\"x%5E2=y\"$ and get a quadratic equation:\r
\n" ); document.write( "\n" ); document.write( " $\"4y%5E2-25y%2B25=0\"$ , solving this equation we find:y=5 and y=5/4.\r
\n" ); document.write( "\n" ); document.write( "Knowing that, $\"x%5E2=5\"$ , get $\"x=sqrt%285%29\"$ and $\"x=-sqrt%285%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Also from $\"x%5E2=5%2F4\"$ , we get $\"x=sqrt%28%285%29%2F2%29\"$ and $\"x=-sqrt%28%285%29%2F2%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Thus, the solution set is:[ $\"sqrt%285%29\"$ , $\"-sqrt%285%29\"$ , $\"sqrt%285%29%2F2\"$ , \r
\n" ); document.write( "\n" ); document.write( " $\"-sqrt%285%29%2F2\"$ ] \n" ); document.write( "

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