Question

the difference of two number is 5 and difference of their reciprocal is 1 by 10 find the numbers​

Answer 1

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Answer 2

Answer: 10 , 5

Step-by-step explanation:

Let the numbers be A & B

B - A = 5

1/A - 1/B = 1/10

B-A/AB = 1/10          [took LCM]

5/AB = 1/10

AB = 5* 10 = 50

We have, difference = 5 && product = 50

50 = 5 * 10

Hence the numbers are 10, 5

ALTERNATE:

Using quadratic equation method

A*B = 50

B - A = 5

B = A+5

A*(A+5) = 50

A^2 + 5A - 50 = 0

Sum = 5 && Product = -50

Numbers are : 10, -5

A^2 -5A + 10A -50 = 0

A(A-5) + 10(A-5) = 0

[A+10][A-5] = 0

A = -10,5

When A = 5, B =10