a = 5√2 - 4√3,
　b = 3√3 - 5,
　c = 3√2 - 4,
とおくと
　3a + 4b - 5c = 0,

∴　a^2 + b^2 - c^2 = (-2a -b +2c)^2 + (c-a)(3a+4b-5c)
　　= (-2a -b +2c)^2
　　= (-3 -4√2 +5√3)^2
　　= {2/(147 + 104√2 + 85√3 + 60√6)}^2
　　≒ (1/294)^2,

∴　a：b：c　≒　3：4：5,

3 + 4√2 ≒ 5√3,
(3/5)√(1/3) + (4/5)√(2/3) ≒ 1,