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Задача Задача №2635363
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Аноним
16 января 2025 16:31 · публичный вопрос
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Аноним

1/8×(-1/8-8)+(-1/8-6)×(-1/8-6)

Ответ нейросети
16 января 2025 16:31

Let's simplify the expression step by step:

The expression is:

\[ \frac{1}{8} \times \left(-\frac{1}{8} - 8\right) + \left(-\frac{1}{8} - 6\right) \times \left(-\frac{1}{8} - 6\right) \]

First, calculate \(-\frac{1}{8} - 8\):

\[ -\frac{1}{8} - 8 = -\frac{1}{8} - \frac{64}{8} = -\frac{1 + 64}{8} = -\frac{65}{8} \]

Now, substitute this back into the expression:

\[ \frac{1}{8} \times \left(-\frac{65}{8}\right) + \left(-\frac{1}{8} - 6\right) \times \left(-\frac{1}{8} - 6\right) \]

Now calculate \(\frac{1}{8} \times -\frac{65}{8}\):

\[ \frac{1}{8} \times -\frac{65}{8} = -\frac{65}{64} \]

Next, calculate \(-\frac{1}{8} - 6\):

\[ -\frac{1}{8} - 6 = -\frac{1}{8} - \frac{48}{8} = -\frac{49}{8} \]

Now we need to compute \(\left(-\frac{49}{8}\right) \times \left(-\frac{49}{8}\right)\):

\[ \left(-\frac{49}{8}\right)^2 = \frac{49^2}{8^2} = \frac{2401}{64} \]

Now we can put it all back into the original expression:

\[ -\frac{65}{64} + \frac{2401}{64} \]

This is equivalent to:

\[ \frac{-65 + 2401}{64} = \frac{2336}{64} \]

Finally, simplify \(\frac{2336}{64}\):

\[ 2336 \div 64 = 36.5 \]

Thus, the final answer is:

\[ \boxed{36.5} \]