Given that a, b, c and d are in geometric progression prove that:
$(b-c)^2 + (c-a)^2 + (d-b)^2 = (a-d)^2$
I've established that ar = b, br = c, cr = d where r is a common ratio.
However I do not understand what my next approach should be.
I've done this, thus far:
Sort of unrelated to this, but is there a quick way to expand expressions like these?
I found this: $a^2r^6-2a^2r^3+a^2$
But how can I divide by $a^2$ if this an expression and not an equation?