document.write( "Question 1012113: if a,b,c in ap nd x,y,z in gp prove that x^b y^c z^a=x^c y^a z^b \n" ); document.write( "
Algebra.Com's Answer #628162 by fractalier(6550)![]() ![]() You can put this solution on YOUR website! Since a, b, and c are in an arithmetic progression, we can write them as \n" ); document.write( "a, a + d, and a + 2d. \n" ); document.write( "Since x, y, and z are in geometric progression , we can write them as \n" ); document.write( "x, xr and xr^2. \n" ); document.write( "Thus we can substitute into \n" ); document.write( "x^b y^c z^a = x^c y^a z^b \n" ); document.write( "and get \n" ); document.write( " \n" ); document.write( "which yields \n" ); document.write( " \n" ); document.write( "Now collect like bases and get \n" ); document.write( " \n" ); document.write( "and we're done... \n" ); document.write( " |