Question

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

Which value is a counterexample to kelvins conjecture?
-1/2
-2
0
5

Answer 1

5

Explanation:

Given inequality,

`x^2 > x + 1`

For
`x=-(1)/(2)`

`(-(1)/(2))^2 > -(1)/(2) + 1`

`\implies (1)/(4) > (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.

Answer 2

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.