Question 167166
the reciprical of x is 1/x.
the reciprical of a/b is b/a
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let x represent the "certain positive number"
Therefore, the reciprical of x is 1/x and 1/x is one less than twice x so:
{{{1/x=2x-1}}}
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Solve for x
multiply both sides by x (remember to put parenthesis around the right side so you do not make an error in multiplying).
{{{1/x*x=x(2x-1)}}}
reduce on the left and distribute on the right side
{{{1=2x^2-x}}}
move all terms to the same side
{{{2x^2-x-1=0}}}
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From here you can either plug this into the Quadratic equation or you can complete the square.
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{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
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{{{x = (-(-1) +- sqrt( (1)^2-4*(2)*(-1) ))/(2*(2)) }}} 
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{{{x = (1 +- sqrt( 1+8 ))/4 }}}
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{{{x=(1+-3)/4}}}
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{{{x=1}}} and {{{x=-1/2}}}
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I hope this helps!
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