Question

Describe each step taken to solve the equation. Then, check the solution to see if it is valid. If it is not a valid solution, explain why∛x-6=4, ∛x=10, x=1000.

Answer 1

x= 1000

Explanation:

We are given the equation ∛x-6=4 and we have to solve the equation for x.

Now, ∛x-6=4 ....... (1)

⇒ ∛x =6+4 {Taking all the constant terms to the right hand side.}

⇒
`x^{(1)/(3) }` =10 {Since, ∛x can also be represented by the symbol
`x^{(1)/(3) }` }

⇒ x = 10³ {We have applied the formula of indices that if
`x^{(1)/(3) }= a,`, then x =a³}

⇒ x= 1000. (Answer)

Now, if we put x =1000 in the equation (1), the we will get Left Hand Side =Right Hand Side. =4 (Answer)