Question

The sum of two numbers is 25.The sum of their reciprocal is 1/4 . Find the two numbers​

Answer 1

Step-by-step explanation:

a + b = 25

1/a + 1/b = 1/4

a + b = ab/4

25 = ab/4

b = 100/a

100/a + a = 25

100 + a^2 = 25a

a^2 - 25a + 100 = 0

(a - 20)(a - 5) = 0

a = 20, b = 5 or a = 5, b = 20

the two numbers are 5 and 20

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