if x= 1¡Ì2 find (x+1/x)3
To find the value of the expression (x + 1/x)^3, we first need to substitute the given value of x into the expression.
Given x = 1/2, we substitute it into the expression:
(1/2 + 1/(1/2))^3
To simplify the expression further, we need to find a common denominator for the two fractions inside the parentheses:
(1/2 + 2/1)^3
Now, we can add the fractions:
(1/2 + 4/2)^3
Simplifying the addition gives us:
(5/2)^3
To cube the fraction, we multiply it by itself twice:
(5/2) * (5/2) * (5/2)
Multiplying the numerators and denominators gives us:
(125/8)
Therefore, the value of the expression (x + 1/x)^3, given x = 1/2, is 125/8.