document.write( "Question 1091492: if a,b,c are in AP, aalnd a,mb,c are in GP then a, m^2b, c are in HP \n" ); document.write( "

Algebra.Com's Answer #705891 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "if $\"a\"$ , $\"b\"$ , $\"c\"$ are in $\"AP\"$ , and $\"a\"$ , $\"mb\"$ , $\"c\"$ are in $\"GP\"$ then $\"a\"$ , $\"m%5E2b\"$ , $\"c\"$ are in $\"HP+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"a\"$ , $\"b\"$ , $\"c\"$ are in $\"AP\"$ hence $\"2b+=+a%2Bc\"$ -------------(1)
\n" ); document.write( " $\"a\"$ , $\"mb\"$ , $\"c\"$ are in $\"GP\"$ hence $\"m%5E2b%5E2+=+ac\"$ ---------------(2)
\n" ); document.write( "divide (2) by (1)\r
\n" ); document.write( "\n" ); document.write( " $\"%28m%5E2b%5E2%29%2F2b+=+ac%2F%28a%2Bc%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28m%5E2b%29%2F2+=+ac%2F%28a%2Bc%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28m%5E2b%29%28a%2Bc%29+=+2ac\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28a%2Bc%29%2Fac+=+2%2F%28m%5E2b%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2%2F%28m%5E2b%29=+1%2Fa+%2B+1%2Fc\"$ \r
\n" ); document.write( "\n" ); document.write( "hence $\"a\"$ , $\"m%5E2b\"$ , $\"c\"$ are in $\"HP+\"$
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