How do I evaluate something like 3070^2-3069^2?
This looks pretty daunting, but the key to this sort of a problem, which has come up a couple of times in previous PAT tests, is to recognise that this expression is actually the difference of two squares. It can be generalised to the problem of evaluating:
x2-y2
which has as its solution:
x2-y2 = (x+y)(x-y)
so in this case:
30702-30692 = (3070+3069)(3070-3069)=(6139)(1)=6139
SC
Related PAT University answers
All answers ▸Question below as would not fit in here
Find all real solutions of (x^2 +4x +3)^(x^2 -6x+8) = 1
Two satellites are in orbit around the Earth. The first is in a geostationary orbit, the second satellite at radius half that of the first. What is the (approximate) period, in hours, of the second satellite?
Derive the mgh approximation for gravitational potential energy.