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If a2 + b2 = 2a + 4b – 5, then what is the value of (a + b)?1. 52. 43. 24. 3 |
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Answer» Correct Answer - Option 4 : 3 Given: a2 + b2 = 2a + 4b – 5 Formula used: (a – b)2 = a2 + b2 – 2ab Calculation: a2 + b2 = 2a + 4b – 5 ⇒ a2 + b2 – 2a – 4b + 5 = 0 ⇒ a2 + b2 – 2a – 4b + 1 + 4 = 0 ⇒ (a2 – 2a + 1) + (b2 – 4b + 4) = 0 ⇒ (a – 1)2 + (b – 2)2 = 0 The above expression is possible only when, (a – 1) = 0, (b – 2) = 0 ⇒ a = 1, b = 2 a + b = 1 + 2 = 3 ∴ The value of a + b is 3 |
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