The sum of a number and its square is 2?

Answer 1

One

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Well, since we are talking about a second-degree equation, we should at least check if there might be another root (it could be the same). The equation is:

x + x^2 = 2

iff x^2 + x - 2 = 0

iff (x+1/2)^2 - 2 - 1/4 = 0

iff (x+1/2)^2 = (3/2)^2

iff x+1/2 = +- 3/2

iff x = -2 or x = 1

Hence, the other solution is -2. Note that -2 + (-2)^2 = -2 + 4 = 2 as required.

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The difference of a number's square and its double is -1? Answer: one (and only one). Check this.

Answer 2

1