Question

The sum of two positive members are 5. And Their sum of reciprocal is 4/21. What are the numbers.
$(x > y) \\ ( \frac{1}{x} < \frac{1}{y} )$

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Answer 1

Answer:

x = 6, y=12 or x = 12 ,y=6

Step-by-step explanation:

Let the numbers be x and y

We are given that the sum of two numbers is 18

So, x+y=18x+y=18 ---1

We are also given that the sum of their reciprocal is 1/4.

So, \frac{1}{x}+\frac{1}{18-x}=\frac{1}{4}x1+18−x1=41

Substitute the value of y from 1

\frac{18-x+x}{x(18-x)}=\frac{1}{4}x(18−x)18−x+x=41

\frac{18}{x(18-x)}=\frac{1}{4}x(18−x)18=41

\frac{18 \times 4}{x(18-x)}=1x(18−x)18×4=1

\frac{72}{18x-x^2}=118x−x272=1

[tex]72=18x-x^2[tex]

[tex]x^2-18x +72=0[tex]

[tex]x^2-12x-6x +72=0[tex]

[tex]x(x-12)-6(x -12)=0[tex]

[tex](x-6)(x-12)=0[tex]

[tex]x=6,12[tex]

when x is 6

y = 18-x=18-6=12

when x is 12

y = 18-x=18-12=6