Question

Find out the value of the given expression ${\left( {x + 1} \right)^3}$ for real x if, ${\left( {x - 1} \right)^3} = 8$.

Answer 1

Hint- Here we will proceed by first solving the given equation in the question and finding the value of x. Then we will substitute the real value of x in ${\left( {x + 1} \right)^3}$ to get to the desired answer.

Complete step-by-step answer:

Given that ${\left( {x - 1} \right)^3} = 8$

Thus, finding the value of x,
${\left( {x - 1} \right)^3} = 8$
$ \Rightarrow {\left( {x - 1} \right)^3} = {2^3}$
 $ \Rightarrow x - 1 = 2$ (cancelling out the common cubes)
$ \Rightarrow x = 2 + 1 = 3$

Therefore,
${\left( {x + 1} \right)^3} = {\left( {3 + 1} \right)^3} = {\left( 4 \right)^3} = 64$

Note - Remember that any method can be used to find x from the first equation.