document.write( "Question 239295: the sum of a number and seven times its reciprocal is 16/3. find the number \n" ); document.write( "
Algebra.Com's Answer #175702 by anantha(86)\"\" \"About 
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sol:
\n" ); document.write( "let the number be x
\n" ); document.write( "its reciprocal=1/x
\n" ); document.write( "7 times its reciprocal=7*1/x=7/x
\n" ); document.write( "according to the problem
\n" ); document.write( "sum of a number and 7 times its reciprocal=16/3
\n" ); document.write( "x+7/x=16/3
\n" ); document.write( "multiply both sides by x
\n" ); document.write( "x*x+7/x*x=16/3*x
\n" ); document.write( "x^2+7=16x/3
\n" ); document.write( "multiply both sides by 3
\n" ); document.write( "x^2*3+7*3=16x/3*3
\n" ); document.write( "3x^2+21=16x
\n" ); document.write( "transpose 16x from R.H.S to L.H.S
\n" ); document.write( "3x^2-16x+21=0
\n" ); document.write( "on multiplying two numbers we get 63 and adding or subtracting two numbers we get 16
\n" ); document.write( "those numbers are 7 and 9
\n" ); document.write( "7*9=63
\n" ); document.write( "and 7+9=16
\n" ); document.write( "3x^2-16x+21=0 can be written as
\n" ); document.write( "3x^2-9x-7x+21=0
\n" ); document.write( "3x(x-3)-7(x-3)=0
\n" ); document.write( "(3x-7)(x-3)=0
\n" ); document.write( "3x-7=0
\n" ); document.write( "3x=7
\n" ); document.write( "x=7/3
\n" ); document.write( "x-3=0
\n" ); document.write( "x=3
\n" ); document.write( "the number is 7/3 or 3\r
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