If a + b + c + d = 2, then the maximum value of (1 + a)(1 + b)(1 + c)(1 + d) is:
A. $$\frac{{91}}{9}$$
B. $$\frac{{81}}{{16}}$$
C. $$\frac{{63}}{{22}}$$
D. $$\frac{{54}}{{13}}$$
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & a + b + c + d = 2 \cr & {\text{Let }}a = b = c = d = \frac{1}{2} \cr & {\text{satisfy the above}} \cr & {\text{so, }}\left( {1 + a} \right)\left( {1 + b} \right)\left( {1 + c} \right)\left( {1 + d} \right) \cr & = \left( {1 + \frac{1}{2}} \right)\left( {1 + \frac{1}{2}} \right)\left( {1 + \frac{1}{2}} \right)\left( {1 + \frac{1}{2}} \right) \cr & = \frac{3}{2} \times \frac{3}{2} \times \frac{3}{2} \times \frac{3}{2} \cr & = \frac{{81}}{{16}} \cr} $$Related Questions on Algebra
If $$p \times q = p + q + \frac{p}{q}{\text{,}}$$ then the value of 8 × 2 is?
A. 6
B. 10
C. 14
D. 16
A. $$1 + \frac{1}{{x + 4}}$$
B. x + 4
C. $$\frac{1}{x}$$
D. $$\frac{{x + 4}}{x}$$
A. $$\frac{{20}}{{27}}$$
B. $$\frac{{27}}{{20}}$$
C. $$\frac{6}{8}$$
D. $$\frac{8}{6}$$
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