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If a + b + c + d = 2, then the maximum value of (1 + a) (1 + b) (1 + c) (1 + d) is _______.1. \(\frac{{91}}{9}\)2. \(\frac{{81}}{16}\)3. \(\frac{{63}}{22}\)4. \(\frac{{54}}{13}\) |
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Answer» Correct Answer - Option 2 : \(\frac{{81}}{16}\) Given: If a + b + c + d = 2. Calculation: If a + b + c + d = 2 For maximum value a = b = c = d ⇒ 4a = 2 ⇒ a = 2/4 ⇒ a = 1/2 Putting the value of a in (1 + a)(1 + b)(1 + c)(1 + d) ⇒ (1 + 1/2)(1 + 1/2)(1 + 1/2)(1 + 1/2) ⇒ (3/2)(3/2)(3/2)(3/2) ⇒ 81/16 ∴ The maximum value of (1 + a) (1 + b) (1 + c) (1 + d) is 81/16. |
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