Question

Determinati solutiile ecuatiilor

Answer 1

Răspuns:

$f) - \frac{7}{3} {x}^{2} = \frac{28}{3} \\ - 7 {x}^{2} = 28 \\ {x}^{2} = 28 \div ( - 7) \\ {x}^{2} = - 4 \\ x1 = \sqrt{ - 4} \: \: ecuatia \: nu \: are \: solutii \: reale \: \\ x2 = - \sqrt{ - 4} \: \: ecuatia \: nu \: are \: solutii \: reale$

$d)2 {x}^{2} = 1 - ( { - 1})^{2} \\ 2 {x}^{2} = 1 + 1 \\ 2 {x}^{2} = 2 \\ {x}^{2} = 1 \\ x1 = \sqrt{1} = 1 \\ x2 = - \sqrt{1} = - 1$

$a)0.1 {x}^{2} = 2.5 \\ \frac{1}{10} {x}^{2} = \frac{25}{10} \\ {x}^{2} = \frac{25}{10} \div \frac{1}{10} \\ {x}^{2} = \frac{25}{10} \times \frac{10}{1} \\ {x}^{2} = 25 \\ x1 = \sqrt{25} = 5 \\ x2 = - \sqrt{25} = - 5$

$b)0.1 {x}^{2} + 0.02 = 0.003 \\ \frac{1}{10} {x}^{2} + \frac{2}{100} = \frac{3}{1000} \\ \frac{1}{10} {x}^{2} = \frac{3}{1000} - \frac{2}{100} \\ \frac{1}{10} {x}^{2} = \frac{3}{1000} - \frac{20}{1000} \\ \frac{1}{10} {x}^{2} = - \frac{17}{1000} \\ \frac{100 {x}^{2} }{1000} = \frac{ - 17}{1000} \\ 100 {x}^{2} = - 17 \\ {x}^{2} = \frac{ - 17}{100} \\ {x}^{2} = - 0.17 \\ x1 = \sqrt{ - 0.17} \: ecuatia \: nu \: are \: solutii \: reale \\ x2 = - \sqrt{ - 0.17} \: ecuatia \: nu \: are \: solutii \: reale$

$c)29( {x}^{2} - 3) =0 | \div 29 \\ \ {x}^{2} - 3 = 0 \\ {x}^{2} = 3 \\ x1 = \sqrt{3} \\ x2 = - \sqrt{3}$

$e) \frac{1}{4} {x}^{2} + 2 = \frac{51}{25} \\ \frac{25 {x}^{2} }{100} + \frac{200}{100} = \frac{51 \times 4}{100} \\ \frac{25 {x}^{2} + 200 }{100} = \frac{204}{100} \\ 25 {x}^{2} + 200 = 204 \\ 25 {x}^{2} = 4 \\ {x}^{2} = \frac{4}{25} \\ x1 = \sqrt{ \frac{4}{25} } = \frac{2}{5} \\ x2 = - \sqrt{ \frac{4}{25} } = - \frac{2}{5}$

$g)0.03 {x}^{2} + 0.17 = \frac{11}{25} \\ \frac{3 {x}^{2} }{100} + \frac{17}{100} = \frac{44}{100} \\ 3 {x}^{2} + 17 = 44 \\ 3 {x}^{2} = 27 \\ {x}^{2} = 9 \\ x1 = \sqrt{9} = 3 \\ x2 = - \sqrt{9} = - 3$

$h) \frac{1}{2} {x}^{2} + 0.5 = \sqrt{0.25} \\ \frac{ {x}^{2} }{2} + 0.5 = \sqrt{ \frac{25}{100} } \\ \frac{ {x}^{2} }{2} + 0.5 = \frac{5}{10} \\ \frac{5 {x}^{2} }{10} + \frac{5}{10} = \frac{5}{10} \\ 5 {x}^{2} + 5 = 5 \\ 5 {x}^{2} = 0 \\ {x}^{2} = 0 \\ x = 0$