Question

Se, x + y = 9 e, x² + y² = 54 , qual e o valor de x - y

Answer 1

$\text x+\text y=9 \ \ ; \ \ \text x^2+\text y^2=54 \ \ ; \ \ \text x-\text y = \ ? \\\\\\ \text{Fa{\c c}amos}: \\\\ (\text x+\text y)^2=\text x^2+\text y^2+2\text{xy} \\\\ 9^2=54+2\text{xy} \\\\ 81 -54 = \text{2xy} \\\\\ 2\text{xy} = 27 \\\\ \underline{\text{Da{\'i}}}: \\\\ (\text x-\text y) ^2=\text x^2+\text y^2-2\text{xy} \\\\ (\text x-\text y)^2=54-27 \\\\ \text x-\text y=\sqrt{27}\to \text x- \text y=\sqrt{9.3} \\\\\ \huge\boxed{\text x-\text y =3\sqrt{3} \ } \checkmark$