How do you prove that x squared + x +1 is positive for all values of x?

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How do you prove that x squared + x +1 is positive for all values of x?

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## Answers (2)

x^2 + x +1 is always positive.

I think it can be proved by trying to shape the possible negative contributor " x" into perfect share shape.

addling and subtracting c'=b^2/4a (perfect square condition)

c' = 1/4

x^2 + x +1+(1/4) - (1/4) Taking +ve along into square

[ x + (b/2a)]^2 + (constant) form

[ x + (1/2)]^2 + [(1-(1/4)]

[ x + (1/2)]^2 + [3/4]

Now whatever be x, any negative integer or non-integer, the square term will always be positive and other hanging along (3/4) term is die-hard positive.

PROVED: The above answerer's are also true but iteratively and younger students will remain baffled by iteration, whereas showing them square magic will be like - snake charming (algebra is known COBRA of maths).

that would be four and four is a positive number not a negative four so x= positive