Question

2^x [(x+1)^3 -1] =2^x - (x+1)^3 + 1

Evaluate the expression of both of the whole number X values. One will be negative and the other positive. Identify the negative value as a lower bound and a positive value as a upper bound.

Answer 1

Explanation:

Given

2^x [(x+1)³ -1] = 2^x - (x+1)³ + 1

Lep p = 2^x, and q = (x+1)³ - 1

Then the original equation becomes

pq = p - q

p - q - pq = 0

p(1 - q) - q = 0

p = q/(1 - q)

2^x = [(x+1)³ - 1]/[-(x+1)³]

2^x = [1 - (x+1)³]/[(x+1)³]

2^x = (x+1)^(-3) - 1