$\\$
`2a^2 + 9b^2 + 6ab - 14a - 30b +29=0`
`-> (a^2 + 6ab + 9b^2) - (10a + 30b) + 25 + a^2 - 4a + 4=0`
`-> (a+3b)^2 - 2 . (a +3b) . 5 + 5^2 +(a^2 - 4a+4)=0`
`-> (a+3b - 5)^2 + (a-2)^2=0`
Vì `(a+3b-5)^2 ≥0, (a-2)^2 ≥0∀a,b`
`-> (a+3b-5)^2 + (a-2)^2 ≥0∀a,b`
Dấu "`=`" xảy ra khi :
`↔ (a+3b-5)^2=0, (a-2)^2=0`
`↔a+3b=5, a=2`
`↔ 2+3b=5, a=2`
`↔b=1,a=2`
`S=(a-1)^{2021} - (1-b)^{2021}`
`->S = (2-1)^{2021} - (1-1)^{2021}`
`->S=1`
Vậy `S=1`
