Question

cum se face (x-1)(x-2)=12 va rog explicații rezolvare nu rezultat direct

Answer 1

fara formula  radacinilor ecuatiei de grad 2
x²-2x-x+2=12
x²-3x+2-12=0
x²-3x-10=0
x²+2x-5x-10=0
x(x+2)-5(x+2)=0
(x+2)(x-5)=0
pt ca un produs sa fie 0, trebuie ca unul din factori sa fie 0
x+2=0
x=-2

x-5=0
x=-5
x∈{-5;2}


Cu formula radacinilor ecuatiei de  grad 2
x²-3x-10=0
x1,2=(3+/-√(9+40))/2=(3+/-7)/2
x1=-4/2=-2
x2=10/2=5
x∈{-2;5}

Answer 2

$(x - 1)(x - 2) = 12$

$x \times x + x \times ( - 2) - 1 \times x - 1 \times ( - 2) = 12$

${x}^{2} - 2x - x + 2 = 12$

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

${x}^{2} - 3x - 10 = 0$

$a = 1$

$b = - 3$

$c = - 10$

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

$\Delta = {( - 3)}^{2} - 4 \times 1 \times ( - 10)$

$\Delta = 9 + 40$

$\Delta = 49 > 0 = > \exists \: x_{1} \: \neq \: x_{2}$

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

$x_{1,2}=\frac{-(-3)\pm\sqrt{49}}{2\times1}$

$x_{1,2}=\frac{3\pm7}{2}$

$x_{1}=\frac{3 + 7}{2}$

$x_{1}=\frac{10}{2}$

$x_{1}=5$

$x_{2}=\frac{3 - 7}{2}$

$x_{2}= - \frac{4}{2}$

$x_{2}=-2$