Question

O conjunto solução da equação x² – 3.x 10 = 0, é:

Answer 1

Resposta:

x₁ = 5, x₂ = -2

Explicação passo-a-passo:

$x^2-3x-10=0\\x_{1,\:2}=\frac{-\left(-3\right)\pm \sqrt{\left(-3\right)^2-4\cdot \:1\cdot \left(-10\right)}}{2\cdot \:1}\\x_{1,\:2}=\frac{-\left(-3\right)\pm\sqrt{3^2+4\cdot \:1\cdot \:10}}{2\cdot \:1}\\x_{1,\:2}=\frac{-\left(-3\right)\pm \sqrt{49}}\\\\x_{1,\:2}=\frac{-\left(-3\right)\pm \:7}{2\cdot \:1}$

$x_1=\frac{-\left(-3\right)+7}{2\cdot \:1},\:x_2=\frac{-\left(-3\right)-7}{2\cdot \:1}$

$x_1=\frac{-\left(-3\right)+7}{2\cdot \:1}\\x_1=\frac{3+7}{2\cdot \:1}\\x_1=\frac{10}{2}\\x_1=5$

$x_2=\frac{-\left(-3\right)-7}{2\cdot \:1}\\x_2=\frac{3-7}{2\cdot \:1}\\x_2=-\frac{4}{2}\\x_2=-2$

$x_1=5,\:x_2=-2$