Ta có: $\dfrac{x}{3}$ = $\dfrac{y}{7}$
⇒ $\dfrac{x^2}{3^2}$ = $\dfrac{y^2}{7^2}$
⇒ $\dfrac{x^2}{9}$ = $\dfrac{y^2}{49}$
Áp dụng dãy tỉ số bằng nhau, có:
$\dfrac{x^2}{9}$ = $\dfrac{y^2}{49}$ = $\dfrac{x^2 - y^2}{9 - 49}$
mà `x² - y² = - 160`
⇔ $\dfrac{x^2}{9}$ = $\dfrac{y^2}{49}$ = $\dfrac{-160}{-40}$ `= 4`
⇔ $\dfrac{x^2}{9}$ `= 4 ⇔ x² = 36 ⇔ x ∈ {6; -6}`
$\dfrac{y^2}{49}$ `= 4 ⇔ y² = 144 ⇔ x ∈ {12; -12}`
