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If (a + b – 6)2 + a2 + b2 + 1 + 2b = 2ab + 2a, then the value of a is
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- 7
- 6
- 3.5
- 2.5
Correct Option: C
(a + b – 6)2 + a2 + b2 + 1 + 2b = 2ab + 2a
⇒ (a + b – 6)2 + a2 + b2 +1 + 2b – 2ab – 2a = 0
⇒ (a + b – 6)2 + (a)2 + (–b)2 + (–1)2 + 2a (–b) + 2 (–b) (–1) + 2 (a) (–1) = 0
⇒ (a + b – 6)2 + (a – b – 1)2 = 0
⇒ a + b – 6 = 0 and a – b – 1 = 0
⇒ a + b = 6 and a – b = 1
On adding these two equations,
a + b + a – b = 6 + 1
⇒ 2a = 7
| ⇒ a = | = 3.5 | |
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