Question

If x3 + 3x2 + 9x = 1, then the value of x3 + 3/x​

Answer 1

Step-by-step explanation:

There is, however, a local minimum.

y=(x+1)3−12(x+1)+12

This has a local maximum for some x<−1 and a local minimum for some x>−1 .

We can pin the values down more precisely.

y′=3(x+1)2−12

with stationary points where y′=0 , or 3(x+1)2=12 , or (x+1)=±2 ; it's easy to verify that x=−3 is a local maximum and x=1 is a local minimum. For x=1 , y=−4 .

Answer 2

(((x3) - 3x2) - 9x) - 1 = 0

:

Checking for a perfect cube

2.1 x3-3x2-9x-1 is not a perfect cube

Trying to factor by pulling out :

2.2 Factoring: x3-3x2-9x-1

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: -9x-1

Group 2: -3x2+x3

Pull out from each group separately :

Group 1: (9x+1) • (-1)

Group 2: (x-3) • (x2)