Question

If a+b+c+d=1 then the maximum value of (1+a)(1+b)(1+c)(1+d) is

Answer 1

Answer:

1.25⁴ = 2.4414

Step-by-step explanation:

The maximum value of (1+a)(1+b)(1+c)(1+d) will be when (1+a)=(1+b)=(1+c)=(1+d)

It will happen when a = b = c = d = 1/4 = 0.25

So (1+a)=(1+b)=(1+c)=(1+d) = 1+0.25 = 1.25

So Maximum value of (1+a)(1+b)(1+c)(1+d) = (1.25)(1.25)(1.25)(1.25) = 1.25⁴ = 24414

Answer 2

Step-by-step explanation:

If a+b+c+d=1, then the maximum value of (1+a)(1+b)(1+c)(1+d)(1+a)(1+b)(1+c)(1+d) is

A) 1

B) (12)3(12)3

C) (34)3(34)3

D) (54)4(54)4

Correct Answer:

D) (54)4(54)4

Description for Correct answer:

a+b+c+d = 1

(1+a)(1+b)(1+c)(1+d)(1+a)(1+b)(1+c)(1+d)

=> For maximum value a, b, c, d

a=b=c=d=14a=b=c=d=14

= = (1+1/4)(1+1/4)(1+1/4)(1+1/4)=(5/4)^4

answer (5/4)^4