Найдите значение корня:
а) $\sqrt{\frac{165^2 - 124^2}{164}}$;
б) $\sqrt{\frac{98}{176^2 - 112^2}}$;
в) $\sqrt{\frac{149^2 - 76^2}{457^2 - 384^2}}$;
г) $\sqrt{\frac{145,5^2 - 96,5^2}{193,5^2 - 31,5^2}}$.
$\sqrt{\frac{165^2 - 124^2}{164}} = \sqrt{\frac{(165 - 124)(165 + 124)}{164}} = \sqrt{\frac{41 * 289}{164}} = \sqrt{\frac{289}{4}} = \frac{17}{2} = 8,5$
$\sqrt{\frac{98}{176^2 - 112^2}} = \sqrt{\frac{98}{(176 - 112)(176 + 112)}} = \sqrt{\frac{98}{64 * 288}} = \sqrt{\frac{49}{64 * 144}} = \frac{7}{8 * 12} = \frac{7}{96}$
$\sqrt{\frac{149^2 - 76^2}{457^2 - 384^2}} = \sqrt{\frac{(149 - 76)(149 + 76)}{(457 - 384)(457 + 384)}} = \sqrt{\frac{73 * 225}{73 * 841}} = \sqrt{\frac{225}{841}} = \frac{15}{29}$
$\sqrt{\frac{145,5^2 - 96,5^2}{193,5^2 - 31,5^2}} = \sqrt{\frac{(145,5 - 96,5)(145,5 + 96,5)}{(193,5 - 31,5)(193,5 + 31,5)}} = \sqrt{\frac{49 * 242}{162 * 225}} = \sqrt{\frac{49 * 121}{81 * 225}} = \sqrt{\frac{7 * 11}{9 * 15}} = \frac{77}{135}$
Пожауйста, оцените решение
