- #1
trollcast
Gold Member
- 282
- 13
Homework Statement
Given that a2, b2 and c 2 are in arithmetic progression show that:
$$\frac{1}{b+c} , \frac{1}{c+a} , \frac{1}{a+b} $$
,are also in arthimetic progression.
Homework Equations
The Attempt at a Solution
So I assume by "in arithmetic progression" they mean those are 3 consecutive terms but we can't assume that a2 is the first term?
Then,
$$ b^{2} = a^{2} + d \\ c^2 = b^2 + d \\ c^2 = a^2 + 2d \\ d = b^{2} - a^{2} \\ d = c^{2} - b^{2}$$
However I can't seem to get anything close to what the questions asking me as when I tried solving that set equations I kept on getting equations that just canceled out to 0 as both the sides worked out to be the same?