MCQ
If a2 + b2 + c2 - ab - bc - ca =0, then:
- Aa + b + c
- Bb + c = a
- Cc + a = b
- Da = b = c
✓
Answer
- a = b = c
Solution:
a2 + b2 + c2 - ab - bc - ca = 0
Multiplying by 2 on both the sides, we have
2(a2 + b2 + c2 - ab - bc - ca) = 0
2a2 + 2b2 + 2c2 - 2ab - 2bc - 2ca = 0
a2 + a2 + b2 + b2 + c2 + c2 - 2ab - 2bc - 2ca = 0
(a2 + b2 - 2ab) + (b2 + c2 - 2bc) + (a2 + c2 - 2ac) = 0
(a - b)2 + (b - c)2 + (a - c)2 = 0
(a - b)2 = 0, (b - c)2 = 0, (a - c)2 = 0
(a - b) = 0, (b - c) = 0, (a - c) = 0
a = b, b = c, a = c
or we can say a = b = c
Hence, correct option is (d).
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