Water droplet coalescence - prove S < S1 + S2

[bioinformaticsgirl]

Oh wait. those are for a single variable x, whereas I essentially have an x and a y... Not sure which rule to use here.

0 < (R1 - R2)^2 would give me something close but those 3's I'm not sure what to do with.

 

[haruspex]

Oh wait. those are for a single variable x, whereas I essentially have an x and a y... Not sure which rule to use here.

0 < (R1 - R2)^2 would give me something close but those 3's I'm not sure what to do with.

What's the obvious way to get 3R₁²+3R₂² from R₁²+R₂² ?

 

[Chestermiller]

Using the square of a binomial where (u + v)² = u² - 2uv +v² I would think I can find the sum of terms with this, but I'm not totally sure what to do with those 3's.

I rewrite into standard form:
0 < 3R1² - 2R1R2 + 3R2²

Suppose you wrote $3R_1^2+3R_2^2-2R_1R_2=2R_1^2+2R_2^2+(R_1^2-2R_1R_2+R_2^2)$
Would that help?