If $a = 2022, b = 2021$ and c = 2020, then value of $a^2 + b^2 + c^2 – ab – bc – ca$ is:
Answer & explanation
Correct answer: option 3
We know that,
(a – b)2 = a2 + b2 – 2ab
Given,
a = 2022
b = 2021
c = 2020
= Let, m= a2 + b2 + c2 – ab – bc – ca
= Multiply both sides by 2
= 2m= 2(a2 + b2 + c2 – ab – bc – ca)
= 2m = 2a2 + 2b2 + 2c2 – 2ab – 2bc – 2ca
= 2m = a2 – 2ab + b2 + b2 – 2bc + c2 + c2 – 2ca + a2
= 2X = (a – b)2 + (b – c)2 + (c – a)2
= 2X = (2022 – 2021)2 + (2021 – 2020)2 + (2020 – 2022)2
= 2X = 1 + 1 + 4 = 6
= 2X = 6
= x = 3