Question

2.10. 1) 1/5 x²- -5=0; 3) 1,44-x²-3x²; 5) (2y-1)²-10-4y; 2) 9y²-6,25-0; 4) ¾ x² = −3,5+x³²; 6) (3m-2)(3m+2)=5m².
help plsss, i cnt understnd ths
​

Answer 1

$1) \frac{1}{5} {x}^{2} = 0 + 5 \\ \frac{1}{5} {x}^{2} = 5 \\ {x}^{2} = 5 \div \frac{1}{5} = 5 \times \frac{5}{1} \\ {x}^{2} = 25 \\ x1 = 5 \\ x2 = - 5$

$2)9 {y}^{2} - 6.25 = 0 \\ 9 {y}^{2} = 0 + 6.25 \\ 9 {y}^{2} = 6.25 \\ {y}^{2} = 6.25 \div 9 \\ {y}^{2} = 6 \frac{25}{100} \div 9 = 6 \frac{1}{4} \div 9 \\ {y}^{2} = \frac{25}{4} \times \frac{1}{9} \\ {y}^{2} = \frac{25}{36}$

$y1 = \frac{5}{6} \\ y2 = - \frac{5}{6}$

$3)1.44 - {x}^{2} = 3 {x}^{2} \\ 1.44 - 4 {x}^{2} = 0 \\ 4 {x}^{2} = 1.44 + 0 \\ 4 {x}^{2} = 1.44 \\ {x}^{2} = 1.44 \div 4 \\ {x}^{2} = 0.36 \\ x1 = 0.6 \\ x2 = - 0.6$

$4) \frac{5}{7} {x}^{2} = - 3.5 + {x}^{2} \\ \frac{5}{7} {x}^{2} - {x}^{2} + 3.5 = 0 \\ - \frac{2}{7} {x}^{2} + 3.5 = 0 \\ - \frac{2}{7} {x}^{2} = 0 - 3.5 \\ - \frac{2}{7} {x}^{2} = - 3.5 \\ {x }^{2} = - 3.5 \div ( - \frac{2}{7} )$

${x}^{2} = - 3 \frac{5}{10} \times ( - \frac{7}{2} ) \\ {x}^{2} = - 3 \frac{1}{2} \times( - \frac { 7}{2}) \\ {x}^{2} = - \frac{7}{2} \times ( - \frac{7}{2} ) \\ {x }^{2} = \frac{49}{4} \\ x1 = \frac{7}{2} = 3.5 \\ x2 = \frac{7}{2} = - 3.5$

$5)(2y - 1) {}^{2} = 10 - 4y \\ {4y}^{2} - 4y + 1 = 10 - 4y \\ 4 {y}^{2} - 4y + 1 - 10 + 4y = 0 \\ 4 {y}^{2} - 9 = 0 \\ {4y}^{2} = 0 + 9 \\ {4y}^{2} = 9 \\ {y}^{2} = 9 \div 4 \\ {y}^{2} = \frac{9}{4} \\ y1 = \frac{3}{2} = 1.5$

$y2 = - 1.5$

$6)(3m - 2)(3m + 2) = 5 {m}^{2} \\ {9m}^{2} - 4 - 5 {m}^{2} = 0 \\ {4m}^{2} - 4 = 0 \\ {4m}^{2} = 0 + 4 \\ {4m}^{2} = 4 \\ {m}^{2} = 4 \div 4 \\ {m}^{2} = 1 \\ m1 = 1 \\ m2 = - 1$