Edit to “Решение”

RI_a21 edited
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ru/13.3.3.md +15 −8
@@ -9,27 +9,34 @@Решение
![К задаче $13.3.3$ |1414x753, 100%](../../img/13.3.3/Screenshot 2026-03-29 163121.png)
−\[d_1 + f_1 = 90 \text{ см}\]
−\[x=30 \text{ см}\]
−\[
−\frac{1}{F} = \frac{1}{d_1} + \frac{1}{f_1}
−\]
−\[
−\frac{1}{F} = \frac{1}{d_1+x} + \frac{1}{f_1-x}
−\]
+$$\frac{1}{F} = \frac{1}{d_1 + x} + \frac{1}{f_1 - x}$$
+
$$\frac{1}{d_1} + \frac{1}{f_1} = \frac{1}{d_1 + x} + \frac{1}{f_1 - x}$$
+
$$\frac{f_1 + d_1}{d_1 f_1} = \frac{(f_1 - x) + (d_1 + x)}{(d_1 + x)(f_1 - x)}$$
+
$$\frac{1}{d_1 f_1} = \frac{1}{(d_1 + x)(f_1 - x)}$$
+
$$d_1 f_1 = (d_1 + x)(f_1 - x)$$
+
$$d_1 f_1 = d_1 f_1 - d_1 x + x f_1 - x^2$$
+
$$0 = -d_1 x + x f_1 - x^2$$
+
$$x^2 = x(f_1 - d_1)$$
+
$$x = f_1 - d_1$$
+
$$\frac{1}{F} = \frac{1}{d_1} + \frac{1}{f_1}$$
+
$$x = f_1 - d_1$$
+
$$F = \frac{d_1 f_1}{d_1 + f_1}$$
+
$$F = \frac{(d_1 + f_1)^2 - x^2}{4(d_1 + f_1)}$$
+
$$F = \frac{90^2 - 30^2}{4 \cdot 90} = 20 \text{ см}$$
+
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