Can you express this in form 1 a + 1 b Can you express the...

Augustus Acevedo

Augustus Acevedo

Answered

2022-07-15

Can you express this in form 1 a + 1 b
Can you express the fraction 1949 1999 in the form 1 a + 1 b ? Give reasons supporting your answer.
I think the only way to do this is keep trying numbers but then I will never get the answer. I cry every time.

Answer & Explanation

Karla Hull

Karla Hull

Expert

2022-07-16Added 20 answers

1 a + 1 b = a + b a b ,
so you would need a b to divide 1999. But…
Logan Wyatt

Logan Wyatt

Expert

2022-07-17Added 5 answers

Given
1 a + 1 b = 1949 1999
Combining the fraction gives
a + b a b = 1949 1999
Setting terms gives the system
{ a + b = 1949 a b = 1999
With a , b can be solved by a quadratic. Namely
b 2 1949 b + 1999
b 2 1949 b + 1999
Where a = 1949 b
Since 1999 cannot be factored, the roots are really ugly looking numbers. Namely, the two possible values of b are
b 1 = 1949 + 3790605 2 b 2 = 1949 3790605 2
and with the a values as
a 1 = 1949 3790605 2 a 2 = 1949 + 3790605 2

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