Question

Qual é o valor real x que torna a expres-
são √x^2- x + 4 igual a 4?​

Answer 1

Resposta:

x = 4 ou x = -3

Explicação passo-a-passo:

$\sqrt{x^{2}-x+4} =4\\\sqrt{16} =4\\ x^{2}-x+4 = 16\\ x^{2}-x+4-16=0\\ x^{2}-x-12=0$

Resolver a equação utilizando a fórmula de Bhaskara, sendo que $a=1$, $b=-1$ e $c=-12$:

$x'=\frac{-b+\sqrt{b^{2}-4ac}}{2a}\\\\x'=\frac{-(-1)+\sqrt{(-1)^{2}-4(1)(-12)}}{2(1)}\\\\x'=\frac{1+\sqrt{1-(-48)}}{2}\\\\x'=\frac{1+\sqrt{1+48}}{2}\\\\x'=\frac{1+\sqrt{49}}{2}\\\\x'=\frac{1+7}{2}\\\\x'=\frac{8}{2}\\\\x'=4$

$x"=\frac{-b-\sqrt{b^{2}-4ac}}{2a}\\\\x"=\frac{-(-1)-\sqrt{(-1)^{2}-4(1)(-12)}}{2(1)}\\\\x"=\frac{1-\sqrt{1-(-48)}}{2}\\\\x"=\frac{1-\sqrt{1+48}}{2}\\\\x"=\frac{1-\sqrt{49}}{2}\\\\x"=\frac{1-7}{2}\\\\x"=\frac{-6}{2}\\\\x'=-3$