Question

resolva a equações 25x2-25x+6=0​

Answer 1

Olá, boa noite!

$25 {x}^{2} - 25x + 6 = 0 \\ \\ a = 25 \\ b = ( - 25) \\ c = 6 \\ \\ \Delta = {b}^{2} - 4ac \\ \Delta = {( - 25)}^{2} - 4 \times 25 \times 6 \\ \Delta = 625 - 100 \times 6 \\ \Delta = 625 - 600 \\ \Delta = 25 \\ \\ x = \frac{ - b\pm \sqrt{\Delta} }{2a} \\ \\ x = \frac{ - ( - 25)\pm \sqrt{25} }{2 \times 25} \\ \\ x = \frac{25\pm5}{50} \\ \\ x_{1} = \frac{25 + 5}{50} = \frac{ {30}^{ \color{red} { \div 10}} }{ {50}^{ \color{red} { \div 10}} } = \bf{ \frac{3}{5} } \\ \\ x_{2} = \frac{25 - 5}{50} = \frac{ {20}^{ \color{red} { \div 10}} }{ {50}^{ \color{red} { \div 10}} } = \bf{ \frac{2}{5} }$

$\boxed{\bf{S = \{ \frac{2}{5} , \: \frac{3}{5} \} } }$

Espero ter ajudado! :)