Задание 13, стр 22

Question

Вычислите, применив формулу сокращённого умножения:
$$\mathrm{a})\sqrt{\frac{165^{2}-124^{2}}{164}}\quad  \mathrm{b}) \sqrt{\frac{98}{176^{2}-112^{2}}}\quad \mathrm{c})\sqrt{\frac{149^{2}-76^{2}}{457^{2}-384^{2}}}$$

Gimli · Accepted Answer

\begin{enumerate}[label=(alph*)]
\item $$\sqrt{\frac{165^{2}-124^{2}}{164}}=\sqrt{\frac{(165-124)(165+24)}{164}}=\sqrt{\frac{41 \cdot 289}{164}}=\sqrt{\frac{289}{4}}=\frac{\sqrt{289}}{\sqrt{4}}=\frac{17}{2}=8,5.$$
\item $$\sqrt{\frac{98}{176^{2}-112^{2}}}=\sqrt{\frac{98}{(176-112)(176+112)}}=\sqrt{\frac{98}{64 \cdot 288}}=\sqrt{\frac{49}{64 \cdot 144}}=\frac{7}{\sqrt{64}\cdot \sqrt{144}} = \frac{7}{8\cdot 12} = \frac{7}{96}.$$
\item $$\sqrt{\frac{149^{2}-76^{2}}{457^{2}-384^{2}}}=\sqrt{\frac{(149-76)(149+76)}{(457-384)(457+384)}}=\sqrt{\frac{73\cdot 225}{73\cdot 841}}=\sqrt{\frac{225}{841}}=\frac{15}{29}.$$
\end{enumerate}

Задание 13, стр 22

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Задание 13, стр 22

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