50 is divided into two parts such that the sum of their reciprocal is 1/12.find the two parts .

by cutekitty

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50 is divided into two parts such that the sum of their reciprocal is 1/12.find the two parts .

by cutekitty

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lets say first number is x and second number is (50-x)

so, 50 + 1/(50-x) = 1/12

50 is divided into two parts.

lets say first number is x and second number is (50-x)

so, 50 + 1/(50-x) = 1/12

(50-x+x)/x(50-x) = 1/12

=50/50x-x^2 = 1/12

Now do the cross multiplication

=50x-x^2=600

=x^2-50x+600=0

=(x-30)(x-20) = 0

so, x= 30 or 20

The two parts are 30 and (50-x) = 20.

As per the given question,

(1/(50-x))+(1/x)=1/12.

On solving this we get the two parts as 20 and 30.