Вправа 1347 алгебра Бевз гдз 7 клас
№ 1347
Обчислимо.
a)
$$
24^2-14^2=(24-14)(24+14)=10 \cdot 38=380
$$
б)
$$
62^2-38^2=(62-38)(62+38)=24 \cdot 100=2400
$$
в)
$$
98^2-97^2=(98-97)(98+97)=1 \cdot 195=195
$$
г)
$$
52,5^2-48,5^2=(52,5-48,5)(52,5+48,5)=4 \cdot 101=404
$$
ґ)
$$
14,3^2-4,3^2=(14,3-4,3)(14,3+4,3)=10 \cdot 18,6=186
$$
e)
$$
\begin{gathered}
\left(17 \frac{3}{4}\right)^2-\left(16 \frac{3}{4}\right)^2=\left(\frac{71}{4}\right)^2-\left(\frac{67}{4}\right)^2=\left(\frac{71}{4}-\frac{67}{4}\right)\left(\frac{71}{4}+\frac{67}{4}\right)= \\
\left(\frac{4}{4}\right) \cdot\left(\frac{138}{4}\right)=1 \cdot 34,5=34,5
\end{gathered}
$$
є)
$$
\begin{gathered}
\left(7 \frac{2}{3}\right)^2-\left(2 \frac{1}{3}\right)^2=\left(\frac{23}{3}\right)^2-\left(\frac{7}{3}\right)^2= \\
\left(\frac{23}{3}-\frac{7}{3}\right) \cdot\left(\frac{23}{3}+\frac{7}{3}\right)=\left(\frac{16}{3}\right) \cdot\left(\frac{30}{3}\right)=\frac{16}{3} \cdot 10=160 / 3=53 \frac{1}{3}
\end{gathered}
$$
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