Question

Given that x is a number there is not negative Kelvin conjectured that x(to the 2nd power) > x+1

Answer 1

The way this is written, you cannot use -1/2 or -2. Is that correct? Both of them are minus. So the only things you have going for you is 0 and 5

x^2 > x + 1  when x = 5

5^2 > 5 + 1 and his conjecture is true.

25 > 6

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What about 0?

0^2 = 0   so

0 > 0 + 1 and the conjecture is false.

Answer 2

Answer:

5

Step-by-step explanation:

Given inequality,

$x^2 > x + 1$

For $x=-\frac{1}{2}$

$(-\frac{1}{2})^2 > -\frac{1}{2} + 1$

$\implies \frac{1}{4} > \frac{1}{2}$ ( False )

For $x=-2$

$(-2)^2 > -2 + 1$

$\implies 4 > 1$ ( true )

For $x=0$

$(0)^2 > 0+ 1$

$\implies 0 > 1$ ( False )

For $x=5$

$(5)^2 > 5 + 1$

$\implies 25 > 6$ ( True )

Thus, x = -2 and 5 are the solutions of the given inequality,

But, negative numbers are not allowed.

Hence, x = 5 is a counterexample to kelvins conjecture.