Question

5 Determinați x = R pentru care 4x² + 12 = 4(4x² - 9).​

Answer 1

Explicație pas cu pas:

$4 {x}^{2} + 12 = 4(4 {x}^{2} - 9)$

$4 {x}^{2} + 12 = 16 {x}^{2} - 36$

$16 {x}^{2} - 4 {x}^{2} = 12 + 36$

$12 {x}^{2} = 48 \ \Big|:12$

${x}^{2} = 4 \iff {x}^{2} = {2}^{2} \implies |x| = 2$

$x_{1} = - 2$

$x_{2} = 2$

Answer 2

$\displaystyle 4x^2+12=4\Big(4x^2-9\Big)\Rightarrow 4x^2+12=16x^2-36 \Rightarrow \\\\ \Rightarrow 4x^2-16x^2=-36-12 \Rightarrow -12x^2=-48 \Rightarrow x^2=\frac{48}{12} \Rightarrow x^2=4 \Rightarrow \\\\ \Rightarrow x=\pm\sqrt{4} \Rightarrow x=\pm 2$