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

Question

asked Jul 18, 2019 49.4k views

2 Answers

PhoenixBlue · Answer 1 · 2019-07-20T13:32:15+0000

Answer:

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.

Aronadaal · Answer 2 · 2019-07-23T16:34:40+0000

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.