document.write( "Question 1086719: If x^4+y^4=2 and x^8+y^8=3, what is the value of x^(16)+y^(16) \n" ); document.write( "
Algebra.Com's Answer #700956 by MathTherapy(10552)\"\" \"About 
You can put this solution on YOUR website!
If x^4+y^4=2 and x^8+y^8=3, what is the value of x^(16)+y^(16)
\n" ); document.write( "
\"x%5E4+%2B+y%5E4+=+2\" 				  \"x%5E8+%2B+y%5E8+=+3\"\r\n" );
document.write( "\"%28x%5E4+%2B+y%5E4%29%5E2+=+2%5E2\" ------ Squaring both sides\r\n" );
document.write( "\"x%5E8+%2B+2x%5E4y%5E4+%2B+y%5E8+=+4\" \r\n" );
document.write( "\"x%5E8+%2B+y%5E8+%2B+2x%5E4y%5E4+=+4\" ------ Rearranging terms\r\n" );
document.write( "\"3+%2B+2x%5E4y%5E4+=+4\" ------ Substituting 3 for \"x%5E8+%2B+y%5E8\" \r\n" );
document.write( "\"2x%5E4y%5E4+=+1\" \r\n" );
document.write( "\"x%5E4y%5E4+=+1%2F2\" ------ eq (i)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\"x%5E8+%2B+y%5E8+=+3+\"\r\n" );
document.write( "\"%28x%5E8+%2B+y%5E8%29%5E2+=+3%5E2\" ------ Squaring both sides\r\n" );
document.write( "\"x%5E16+%2B+2x%5E8y%5E8+%2B+y%5E16+=+9\" \r\n" );
document.write( "\"x%5E16+%2B+y%5E16+=+9+-+2x%5E8y%5E8\" \r\n" );
document.write( "\"x%5E16+%2B+y%5E16+=+9+-+2%28x%5E4y%5E4%29%5E2\"\r\n" );
document.write( "\"x%5E16+%2B+y%5E16+=+9+-+2%281%2F2%29%5E2\" ------- Substituting ½ for \"x%5E4y%5E4\" \r\n" );
document.write( "\"x%5E16+%2B+y%5E16+=+9+-+2%281%2F4%29\"\r\n" );
document.write( "
\n" ); document.write( "
\n" );