document.write( "Question 81175This question is from textbook
\n" ); document.write( ": insert two geometric means between 6 and 162 \n" ); document.write( "

Algebra.Com's Answer #58187 by stanbon(75887) $\"\"$ $\"About$

You can put this solution on YOUR website!
insert two geometric means between 6 and 162
\n" ); document.write( "---------
\n" ); document.write( "Let x and y be the two geometric means:
\n" ); document.write( "---------
\n" ); document.write( "EQUATION:
\n" ); document.write( "6/x = x/y = y/162
\n" ); document.write( "Then you have two equation:
\n" ); document.write( "6y=x^2 and y^2=162x
\n" ); document.write( "Solve the 1st for y: y=x^2/6
\n" ); document.write( "Substitute into the 2nd to get:
\n" ); document.write( "(x^2/6)^2=162x
\n" ); document.write( "x^4 = 6^2*162x
\n" ); document.write( "x^4-36*162x=0
\n" ); document.write( "Factor:
\n" ); document.write( "x(x^3-5832)=0
\n" ); document.write( "x^3=5832
\n" ); document.write( "x=18
\n" ); document.write( "-------
\n" ); document.write( "Substitute that into y^2=162x to solve for y
\n" ); document.write( "y^2=162*18
\n" ); document.write( "y=54
\n" ); document.write( "---------
\n" ); document.write( "Then 6/18=18/54=54/162
\n" ); document.write( "18 and 54 are the two geometric means
\n" ); document.write( "==============
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
\n" ); document.write( " \n" ); document.write( "

\n" );