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  • Divide 27 into two parts such that the sum of their reciprocals is  3 /20.        

Divide 27 into two parts such that the sum of their reciprocals is 
3 /20.

 

 
 
 
 
 

Answers (1)

Let 27 divide in two parts x and y 

\because x + y = 27 \\\\ \frac{1}{x} + \frac{1}{y} = \frac{3}{20} \: \: \\\\ solving \: \: this \: \: equation \\\\ xy = 180

BY substitution 

x ( 27-x ) = 180 \\\\ 27 x - x ^2 = 180 \\\\ x ^2 - 27 x + 180 = 0 \\\ \ ( x-12 ) ( x -15 ) = 0 \\\\ x = 12 \: \: or \: \: 15 \\\\ y = 15 \: \: or \: \: 12

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Safeer PP

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