Question

The number 50 is divided into two parts such that the sum of the reciprocals of these parts is 1/12 Find the two parts.​

Answer 1

Answer:

20,30

Step-by-step explanation:

50=x+y

1/x+1/y=1/12

x+y/xy=1/12

50/xy=1/12

xy=600

sum is 50,product is 600

then Two parts 20,30

Answer 2

Answer:

$x = 20 \ or \ x =30$

Step-by-step explanation:

Let the two parts be x and 50 - x

$\frac{1}{x} + \frac{1}{50 - x} = \frac{1}{12}$

$\frac{50}{x(50-x)} = \frac{1}{12}$

$x(50 - x) = 600$

$x^{2} - 50x + 600 = 0$

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

$x = 20 \ or \ x =30$

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