Question

Se x' e x" (com x' > x") são as duas raízes da equação a seguir, o valor da expressão (x' - x") ao quadrado é?

x²- x - 12 = 0


Socorro, preciso da resposta logo ​

Answer 1

$\mathsf{x^2-x-12=0}\\\mathsf{a=1~~~b=-1~~~c=-12}\\\mathsf{\Delta=b^2-4ac}\\\mathsf{\Delta=(-1)^2-4\cdot\,1\cdot(-12)}\\\mathsf{\Delta=1+48}\\\mathsf{\Delta=49}\\\mathsf{x=\dfrac{-b\pm\sqrt{\Delta}}{2a}}\\\mathsf{x=\dfrac{-(-1)\pm\sqrt{49}}{2\cdot\,1}}\\\mathsf{x=\dfrac{1\pm7}{2}}\begin{cases}\mathsf{x'=\dfrac{1+7}{2}=\dfrac{8}{2}=4}\\\mathsf{x''=\dfrac{1-7}{2}=-\dfrac{6}{2}=-3}\end{cases}\\\mathsf{(x'-x'')^2=(4-[-3])^2=(4+3)^2}\\\huge\boxed{\boxed{\boxed{\boxed{\mathsf{7^2=49}}}}}$