x² + 9y² = 6xy ⇒ x² – 6xy + 9y² = 0 ⇒ x² – 2.x.3y + (3y)² = 0 ⇒ (x – 3y)² = 0 ⇒ x – 3y = 0 ⇒ x = 3y ⇒ x : y = 3 : 1
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