Question

Given that x is a nonnegative number, a student conjectured that x+3

Which value of x is a counterexample to the student's conjecture?


X= -1/3

X= -3

X= 2

X= 3

Answer 1

The value of x = -1/3 is a counterexample to the student's conjecture.

Step-by-step explanation:

To find a counterexample to the student's conjecture, we need to find a value of x that does not satisfy the given expression. The expression is x + 3. Let's evaluate the expression for each value of x:

1. x = -1/3: -1/3 + 3 = 2 2/3
2. x = -3: -3 + 3 = 0
3. x = 2: 2 + 3 = 5
4. x = 3: 3 + 3 = 6

From the above calculations, we can see that x = -1/3 is the counterexample to the student's conjecture, as the expression does not equal 3.

Answer 2

`x = 2`

Step-by-step explanation:

Given

Conjecture:
`x + 3 < x^2` --- (Missing)

Required

Which value of x prove the conjecture otherwise

To do this , we simply substitute the values of x in the options

`1.\ x = -(1)/(3)`

This is negative;

So, there is no need to check

`2.\ x = -3`

This is also negative;

So, there is no need to check

`3.\ x = 2`

`x + 3 < x^2`

`2 + 3 < 2^2`

`5 < 4`

This value of x is false because 5 is not less than 4

`4.\ x = 3`

`x + 3 < x^2`

`3 + 3 < 3^2`

`6 < 9`