Given the system of equations
x(x+y)=9
y(x+y)=16
the value of xy can be written as a/b where a and b are positive coprime integers. Find a+b.
x(x+y)=9
y(x+y)=16
the value of xy can be written as a/b where a and b are positive coprime integers. Find a+b.
Answers
Answered by
Steve
we see that 9/x = 16/y, so
y = 16/9 x
x(x + 16/9 x) = 9
25x^2 = 81
x = 9/5 or -9/5
y = 16/5 or -16/5
so, x+y = 5 or -5
check:
9/5 (5) = 9
16/5 (5) = 16
xy = 144/25
a+b = 169
same for - values
y = 16/9 x
x(x + 16/9 x) = 9
25x^2 = 81
x = 9/5 or -9/5
y = 16/5 or -16/5
so, x+y = 5 or -5
check:
9/5 (5) = 9
16/5 (5) = 16
xy = 144/25
a+b = 169
same for - values
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.