Question

Suma inverselor a două numere raționale este , iar diferența inverselor numerelor este . Calculați suma și produsul numerelor.

Answer 1

The sum of the inverses of two rational numbers is 5 by 6, and the difference of the inverses of the numbers is 1 by 6. Calculate the sum and product of numbers.

Sum = a + b = 5

Product = a ₓ b = 6

Explanation:

`(1)/(a) +(1)/(b) =(5)/(6)`

`(1)/(a) -(1)/(b) =(1)/(6)`

Add both equations together

`(1)/(a) +(1)/(a) +(1)/(b) -(a)/(b) =(5)/(6) +(1)/(6)`

2 / a = 6/6

2 / a = 1

a = 2

we replace in any relation a

1 / 2 + 1 / b = 5 / 6

3b + 6 = 5b

5b - 3b = 6

2b = 6

b = 3

Sum = a + b = 2 + 3 = 5

Product = a ₓ b = 2 ₓ 3 = 6