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If a = 2017, b = 2016 and c = 2015, then what is the value of a2 + b2 + c2 – ab – bc – ca? (SSC Sub. Ins. 2017)
- a)–2
- b)0
- c)3
- d)4
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If a = 2017, b = 2016 and c = 2015, then what is the value of a2 + b2 ...
Calculation:
- Given: a = 2017, b = 2016, c = 2015
Formula:
The given expression can be simplified using the formula:
(a^2 + b^2 + c^2 - ab - bc - ca) = 1/2[(a - b)^2 + (b - c)^2 + (c - a)^2]
Substitute values:
- Substitute the given values of a, b, and c into the formula:
= 1/2[(2017 - 2016)^2 + (2016 - 2015)^2 + (2015 - 2017)^2]
= 1/2[(1)^2 + (1)^2 + (-2)^2]
= 1/2[1 + 1 + 4]
= 1/2[6]
= 3
Therefore, the value of a^2 + b^2 + c^2 - ab - bc - ca is 3. Hence, option C (3) is the correct answer.
- Given: a = 2017, b = 2016, c = 2015
Formula:
The given expression can be simplified using the formula:
(a^2 + b^2 + c^2 - ab - bc - ca) = 1/2[(a - b)^2 + (b - c)^2 + (c - a)^2]
Substitute values:
- Substitute the given values of a, b, and c into the formula:
= 1/2[(2017 - 2016)^2 + (2016 - 2015)^2 + (2015 - 2017)^2]
= 1/2[(1)^2 + (1)^2 + (-2)^2]
= 1/2[1 + 1 + 4]
= 1/2[6]
= 3
Therefore, the value of a^2 + b^2 + c^2 - ab - bc - ca is 3. Hence, option C (3) is the correct answer.
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Community Answer
If a = 2017, b = 2016 and c = 2015, then what is the value of a2 + b2 ...
Here, a = 2017, b = 2016, and c = 2015
∴ a2 + b2 + c2 – ab – bc – ca
⇒ (2017)2 + (2016)2 + (2015)2 – 2017× 2016 – 2016 × 2015 – 2015 × 2017 = 3
∴ a2 + b2 + c2 – ab – bc – ca
⇒ (2017)2 + (2016)2 + (2015)2 – 2017× 2016 – 2016 × 2015 – 2015 × 2017 = 3
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