23.1. Find the number which, together with its square, forms the smallest sum.

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(7-8 \text { th) }
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23.1. Let the required number be denoted by $x$. We need to find the value of $x$ for which the expression $x^{2}+x$ takes the smallest value. We have: $x^{2}+x=(x+0.5)^{2}-0.25$. It is clear that the smallest value of this expression is achieved at $x=-0.5$ and it equals $-0.25$.