Question

If x is a real number such that
`x^3 = 729`, then
`x^2+√(x)` equals?

Answer 1

First, we find the value of 'x.'

`x^(3)=729 \\ x= \sqrt[3]{729}`
x=9


`x^(2) + √(x)`

`9^(2)`+
`√(9)`
81+3
= 84

`x^(2) + √(x)`=84

Answer 2

`x^3 = 729 \\ \\ x^2+√(x) =? \\ \\ x^3 - 729=0 \\ \\ x^3-9^3 = 0\\ \\(x-9)(x^2+9x+81)=0`


`x^2+9x+81 =0 \ \ or \ \ x-9 = 0\\ \\\Delta =b^2-4ac =9^2-4\cdot 1\cdot 81=81- 324 =-243 \\ \\ and \ we \ know \ when \ \Delta \ is \ negative, \ theres \ no \ solution \\ or \\ x-9=0 \\ \\x=9`



`a^3-b^3=(a-b)(a^2+ab+b^2) \\\\ \\ x^2+√(x) = 9^2+√(9)=81+3 = 84`