If a = 2022, b = 2021 and c = 2020, then value of a2 + b2 + c2 – ab – bc – ca is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 3
Let, X = a2 + b2 + c2 – ab – bc – ca
Multiply both sides by 2,
⇒ 2X = 2(a2 + b2 + c2 – ab – bc – ca)
⇒ 2X = 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
⇒ X = 6 ÷ 2 = 3
∴ The required value is 3.