Algebra question - prove (1/(a+2))+(1/(b+2))=(1/(c+2))+(1/2) for c>b>a>1

[sirius1910]

Hi,

Would anyone share a proof to the problem below?

(1/(a+2))+(1/(b+2))=(1/(c+2))+(1/2),

Condition is that "c" is bigger than "b" which in turn is bigger than "a" which is bigger than 1

Find all possible solutions (all integers) for a, b and c.

Thanks

 

[Deleted member 4993]

Hi,

Would anyone share a proof to the problem below?

(1/(a+2))+(1/(b+2))=(1/(c+2))+(1/2),

Condition is that "c" is bigger than "b" which in turn is bigger than "a" which is bigger than 1

Find all possible solutions (all integers) for a, b and c.

Thanks

What are your thoughts?

Please share your work with us ...even if you know it is wrong

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[Ishuda]

Hi,

Would anyone share a proof to the problem below?

(1/(a+2))+(1/(b+2))=(1/(c+2))+(1/2),

Condition is that "c" is bigger than "b" which in turn is bigger than "a" which is bigger than 1

Find all possible solutions (all integers) for a, b and c.

Thanks

Well the first thing I would do is change to equivalent conditions:
A=a+2
B=b+2
C=c+2
3<A<B<C
with
\(\displaystyle \frac{1}{A}\, +\, \frac{1}{B}\, = \frac{1}{C}\, +\, \frac{1}{2}\)
and see how that works out.

 

[sirius1910]

Thank you all for your feedback.

I've done a bit of arranging and, by eliminating c through simultaneous equations, arrived at ab = 0 which unfortunately doesn't help given a, b, c are all bigger or equal to 1.

It is this condition 1 <= a <= b <= c that I'm stuck on and was wondering if anyone has managed to solve it.

 

[stapel]

That has no solutions. Do the math and you'll get:
c = 4(a + b + ab) / (4 - ab)
Evident that ab < 4, so can't be a=2 and b=3

However, there are 2 solutions for c > b > a > 0

Thank you all for your feedback.

I've done a bit of arranging and....

It is this condition 1 <= a <= b <= c that I'm stuck on and was wondering if anyone has managed to solve it.

You might want to review the feedback in a bit more depth, especially regarding "this condition". Then ask your instructor if "this condition" was stated correctly in the homework assignment.