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Answer 1

$1, \frac{x}{- 3} = \frac{y}{8} = k, k \neq 0 = > x = - 3 k; y = 8 k M à x^{2} - y^{2} = - \frac{44}{5} = > {(- 3 k)}^{2} - {(8 k)}^{2} = - \frac{44}{5} = > 9 k^{2} - 81 k^{2} = - \frac{44}{5} = > - 72 k^{2} = - \frac{44}{5} = > k^{2} = \frac{11}{90} = > k = \pm \sqrt{\frac{11}{90}} k = \sqrt{\frac{11}{90}} = > x = - 3 \sqrt{\frac{11}{90}}; y = 8 \sqrt{\frac{11}{90}} k = - \sqrt{\frac{11}{90}} = > x = 3 \sqrt{\frac{11}{90}}; y = - 8 \sqrt{\frac{11}{90}} V ậ y (x; y) = \{(- 3 \sqrt{\frac{11}{90}}; 8 \sqrt{\frac{11}{90}}); (3 \sqrt{\frac{11}{90}}; - 8 \sqrt{\frac{11}{90}})\} 2, \frac{x}{5} = \frac{y}{- 4} = \frac{z}{6} = k, k \neq 0 = > x = 5 k; y = - 4 k; z = 6 k M à x y z = 15 = > 5 k . (- 4 k) . 6 k = 15 = > - 120 k^{3} = 15 = > k^{3} = - \frac{1}{8} = > k = - \frac{1}{2} = > x = - \frac{5}{2}; y = 2; z = - 3 V ậ y (x; y; z) = (- \frac{5}{2}; 2; - 3)$

$3, 5 x = 8 y = > \frac{x}{8} = \frac{y}{5} 8 y = 3 z = > \frac{y}{3} = \frac{z}{8} = > \frac{x}{8} = \frac{y}{5}; \frac{y}{3} = \frac{z}{8} = > \frac{x}{24} = \frac{y}{15} = \frac{z}{40} Á p d ụ n g t í n h c h ấ t d ã y t ỉ s ố b ằ n g n h a u t a c ó : \frac{x}{24} = \frac{y}{15} = \frac{z}{40} = \frac{x - 2 y + z}{24 - 2.15 + 40} = \frac{34}{34} = 1 = > x = 24; y = 15; z = 40 V ậ y (x; y; z) = (24; 15; 40)$ .

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Answer 2

$1, \frac{x}{- 3} = \frac{y}{8} = k, k \neq 0 = > x = - 3 k; y = 8 k M à x^{2} - y^{2} = - \frac{44}{5} = > {(- 3 k)}^{2} - {(8 k)}^{2} = - \frac{44}{5} = > 9 k^{2} - 81 k^{2} = - \frac{44}{5} = > - 72 k^{2} = - \frac{44}{5} = > k^{2} = \frac{11}{90} = > k = \pm \sqrt{\frac{11}{90}} k = \sqrt{\frac{11}{90}} = > x = - 3 \sqrt{\frac{11}{90}}; y = 8 \sqrt{\frac{11}{90}} k = - \sqrt{\frac{11}{90}} = > x = 3 \sqrt{\frac{11}{90}}; y = - 8 \sqrt{\frac{11}{90}} V ậ y (x; y) = \{(- 3 \sqrt{\frac{11}{90}}; 8 \sqrt{\frac{11}{90}}); (3 \sqrt{\frac{11}{90}}; - 8 \sqrt{\frac{11}{90}})\} 2, \frac{x}{5} = \frac{y}{- 4} = \frac{z}{6} = k, k \neq 0 = > x = 5 k; y = - 4 k; z = 6 k M à x y z = 15 = > 5 k . (- 4 k) . 6 k = 15 = > - 120 k^{3} = 15 = > k^{3} = - \frac{1}{8} = > k = - \frac{1}{2} = > x = - \frac{5}{2}; y = 2; z = - 3 V ậ y (x; y; z) = (- \frac{5}{2}; 2; - 3)$

$3, 5 x = 8 y = > \frac{x}{8} = \frac{y}{5} 8 y = 3 z = > \frac{y}{3} = \frac{z}{8} = > \frac{x}{8} = \frac{y}{5}; \frac{y}{3} = \frac{z}{8} = > \frac{x}{24} = \frac{y}{15} = \frac{z}{40} Á p d ụ n g t í n h c h ấ t d ã y t ỉ s ố b ằ n g n h a u t a c ó : \frac{x}{24} = \frac{y}{15} = \frac{z}{40} = \frac{x - 2 y + z}{24 - 2.15 + 40} = \frac{34}{34} = 1 = > x = 24; y = 15; z = 40 V ậ y (x; y; z) = (24; 15; 40)$ .

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