Question

Determinați x €R,știind ca (2x-3)la a doua=3

Answer 1

${(2x - 3)}^{2} = 3$

$4 {x}^{2} - 12x + 9 = 3$

$4 {x}^{2} - 12x + 9 - 3 = 0$

$4 {x}^{2} - 12x + 6 = 0 \: | \div 2$

$2 {x}^{2} - 6x + 3 = 0$

$a = 2$

$b = - 6$

$c = 3$

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

$\Delta = {( - 6)}^{2} - 4 \times 2 \times 3$

$\Delta = 36 - 24$

$\Delta = 12$

$x_{1,2}=\frac{-b\pm\sqrt{ \Delta}}{2a}$

$x_{1,2}=\frac{-( - 6)\pm\sqrt{ 12}}{2 \times 2}$

$x_{1,2}=\frac{6\pm2\sqrt{ 3}}{4}$

$x_{1}=\frac{6 + 2\sqrt{ 3}}{4}$

$x_{1}=\frac{2(3+ \sqrt{ 3})}{4}$

$x_{1}=\frac{3 + \sqrt{ 3}}{2}$

$x_{2}=\frac{6 - 2\sqrt{ 3}}{4}$

$x_{2}=\frac{2(3 - \sqrt{ 3})}{4}$

$x_{2}=\frac{(3 - \sqrt{ 3})}{2}$