Question

решите уравнения используя свойства функций
$\sqrt{x - 3} + \sqrt{ \times - 10} = 6$
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Answer 1

$\sqrt{x - 3} + \sqrt{x - 10} = 6 \\ \sqrt{x - 3} = 6 - \sqrt{x - 10} \\ ( \sqrt{x - 3 }) {}^{2} = (6 - \sqrt{x - 10} ) {}^{2} \\ x - 3 = 36 - 12 \sqrt{x - 10} + x - 10 \\ - 3 = 26 - 12 \sqrt{x - 10} \\ 12 \sqrt{x - 10} = 26 + 3 \\ 12 \sqrt{x - 10} = 29 \\ \sqrt{x - 10} = \frac{29}{12} \\ ( \sqrt{x - 10} ) {}^{2} = ( \frac{29}{12} ) {}^{2} \\ x - 10 = \frac{841}{144}$

$x = \frac{841}{144} + 10 \\ x = \frac{2281}{144}$