Question

Given that x is a number that is not negative, Kelvin conjectured that x^2>x+1 .

Which value is a counterexample to Kelvin's conjecture?

−12

−2

0

5

Answer 1

yep its 0   ........................................                 

Answer 2

Answer: x=0  is a counterexample to Kelvin's conjecture.

Explanation:-

Given that x is a number that is not negative, Kelvin conjectured that $x^2>x+1$

A counter example is an example that contradicts or opposes the conjecture.

Thus -12 and -2 cannot be the value of x for the counter example as they are negative

The positive numbers in options are 0 and 5,such that

$0^2>0+1\\\Rightarrow0>1...\text{which is not true.}$

$5^2>5+1\\\Rightarrow25>6...\text{which is true.}$

Thus the value of x=0 contradicts the conjecture made by Kevin.

⇒x=0  is a counterexample to Kelvin's conjecture.