Question

Multimea solutiilor la x la a 2 = 25 si 9(x+3) la a 2 = 16
REPEDE DAU COROANA SI 5 STELE

Answer 1

${x}^{2} = 25$

$x = \pm5$

$S=\left\{-5,5\right\}$

$9 {(x + 3)}^{2} = 16$

$9( {x}^{2} + 6x + 9) = 16$

$9 {x}^{2} + 54x + 81-16 = 0$

$9 {x}^{2} + 54x + 65 = 0$

$a = 9$

$b = 54$

$c = 65$

$\Delta = {b}^{2} - 4ac$

$\Delta = {54}^{2} - 4 \times 9 \times 65$

$\Delta = 2916 - 2340 = 576$

$x_{1,2}=\frac{-b\pm\sqrt{\Delta}}{2a} = \frac{ - 54 \pm \sqrt{576} }{2 \times 9} = \frac{ - 54 \pm24}{18}$

$x_{1}= \frac{ - 54 + 24}{18} =- \frac{30}{18} = -\frac{5}{3}$

$x_{2} = \frac{ - 54 - 24}{18} = - \frac{78}{18} = - \frac{13}{3}$

$S=\left\{-\frac{13}{3},-\frac{5}{3}\right\}$