Question

Rezolvati in multimea numerelor reale ecuatia rad(25-x^2)=4

Answer 1

$\sqrt{25 - {x}^{2} } = 4$

Condiție :

$25 - {x}^{2} \geqslant 0$

$\sqrt{25 - {x}^{2} } = 4 \: | {( \: \: )}^{2}$

$25 - {x}^{2} = 16$

$- {x}^{2} = 16 - 25$

$- {x}^{2} = - 9 \: | \times ( - 1)$

${x}^{2} = 9$

$x = \pm3$

$x_{1}=3 \: verifica \: conditia$

$x_{2}= - 3 \: verifica \: conditia$

Answer 2

C. E. : 25-x² > 0

Ridicam ambele parti ale ecuatiei la patrat.

=>

25-x² = 16

-x² = 16-25

-x² = -9

x² = 9

x1 = 3 si x2 = -3

Ambele solutii verifica conditia.