take v as root over .?

Question

(v3) ^ (2) = (14/3) ^ (2) - (13/3) ^ (2)
(v2) ^(2) = (c) ^ (2) - (b) ^ (2).
there would be infinite sets of c and b find one(either a integer or a rational number)

Answer 1

[sqrt(2)]^2 = c^2 - b^2
Let c = 3/2 and b = 1/2, then
[sqrt(2)]^2 = (3/2)^2 - (1/2)^2
2 = 9/4 - 1/4
2 = 8/4
2 = 2

Answer 2

I'm assuming that the first one is v -sub- 3 and the second is v -sub- 2.

Both deal with the difference of two squares. a^2-b^2 = (a+b)(a-b). (v3)^2 = (14/3 + 13/3) (14/3 - 13/3). (v3)^2 = (27/3)(1/3) = 3. v3 = sqrt (3)

the second equation is very much akin to Pythagoras' Theorem.

Let's call it 5, 12, 13. v3 = 5 if c = 13 & b = 12.