Answer:
x= 5 is the ONLY solution for the given expression and x≠ (-5)
Step-by-step explanation:
The given expression can be written as the following
[tex]x^{3} = {125} \sqrt[3]{x^{3} } = \sqrt[3]{125}[/tex]
which implies x = 5 and x = -5
Now, here the given is [tex]x^{3} = 125[/tex]
and we need to find the value of x.
So, we cube root both the sides.
We get, [tex]\sqrt[3]{x^{3} } = \sqrt[3]{125 }[/tex]
now, 125 = 5 x 5 x 5 = [tex](5)^{3}[/tex]
So, given expression becomes [tex]\sqrt[3]{x^{3} } = \sqrt[3]{(5)^{3}}[/tex]
or, on simplifying, we get
[tex]x^ {3 \times {\frac{1}{3} }} = 5^ {3 \times {\frac{1}{3} }}[/tex]
or, x = 5
hence, x= 5 is the ONLY solution for the given expression.
Because if x = -5 then [tex]x^{3} = (- 5) \times (-5) \times (-5) = -125 \neq 125[/tex]
