Question

2- корень из 3 - x = x - 1 Корень из x+5 + корень из 20-x = 7

Answer 1

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$2 - \sqrt{3 - x} = x - 1 \\ 3 - x = \sqrt{3 - x} \\ {(3 - x)}^{2} = {( \sqrt{3 - x} )}^{2} \\ 9 - 6x + {x }^{2} = 3 - x \\ {x}^{2} - 5x + 6 = 0 \\ d = 25 - 4 \times 6 = 25 - 24 = 1 \\ x1 = \frac{5 + 1}{2} = \frac{6}{2} = 3 \\ x2 = \frac{5 - 1}{2} = \frac{4}{2} = 2$
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$\sqrt{x + 5} + \sqrt{20 - x} = 7 \\ {(\sqrt{x + 5} + \sqrt{20 - x})}^{2} = {7}^{2} \\ x + 5 + 2 \sqrt{(x + 5)(20 - x)} + 20 - x = 49 \\ 25 + 2 \sqrt{20x - {x}^{2} + 100 - 5x } = 49 \\ 2 \sqrt{15x - {x}^{2} + 100 } = 49 - 25 \\ 2 \sqrt{15x - {x}^{2} + 100 } =24 \: \: \: \: \: | \div 2 \\ \sqrt{15x - {x}^{2} + 100 } =12 \\ {( \sqrt{15x - {x}^{2} + 100} )}^{2} = {12}^{2} \\ 15x - {x}^{2} + 100 = 144 \\ - {x}^{2} + 15x - 44 = 0 \\ d = 225 + 4 \times ( - 44) = 225 - 176 = 49 \\ x1 = \frac{ - 15 + \sqrt{49} }{ - 2} = \frac{ - 15 + 7}{ - 2} = \frac{ - 8}{ - 2} = 4 \\ x2 = \frac{ - 15 - \sqrt{49} }{ - 2} = \frac{ - 15 - 7}{ - 2} = \frac{ - 22}{ - 2} = 11$