document.write( "Question 433510: The reciprocal of 5 less than a number is 4 times the reciprocal of twice the number. Find the number. \n" ); document.write( "

Algebra.Com's Answer #300501 by stanbon(75887) $\"\"$ $\"About$

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The reciprocal of 5 less than a number
\n" ); document.write( "is 4 times the reciprocal of twice the number.
\n" ); document.write( "Find the number.
\n" ); document.write( "-----------------------
\n" ); document.write( "Let the number be \"x\":
\n" ); document.write( "Equation:
\n" ); document.write( "x - (1/5) = 4(1/(2x))
\n" ); document.write( "--------------------------
\n" ); document.write( "(5x-1)/5 = 2/x
\n" ); document.write( "-----
\n" ); document.write( "Cross-multiply to get:
\n" ); document.write( "5x^2-x = 10
\n" ); document.write( "5x^2-x-10 = 0
\n" ); document.write( "------
\n" ); document.write( "x = [1+- sqrt(1-4*5*-10)]/10
\n" ); document.write( "---
\n" ); document.write( "x = [1+- sqrt(1+200)]/10
\n" ); document.write( "---
\n" ); document.write( "x = [1+- sqrt(201)]/10
\n" ); document.write( "-----------------------------------
\n" ); document.write( "x = (1+sqrt(201))/10 or x = (1-sqrt(201))/10
\n" ); document.write( "---
\n" ); document.write( "x = 1.518 or x = -1.318
\n" ); document.write( "========================
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
\n" ); document.write( "============
\n" ); document.write( " \n" ); document.write( "

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