Which of the following given option is correct regarding given statement.

Statement I: x^{2} - 8x + 15 = 0.

Statement II: 3y^{2} - 30y + 63 = 0

Option 3 : x = y or relation cannot be established

**Given:**

x2 - 8x + 15 = 0, and

3y2 - 30y + 63 = 0

**Calculation:**

**Statement I: x2 - 8x + 15 = 0.**

⇒ x2 - 8x + 15 = 0

⇒ x2 - (5 + 3)x + 15 = 0

⇒ x2 - 5x - 3x + 15 = 0

⇒ (x - 5)(x - 3) = 0

⇒** x = 5, 3**

**Statement II: 3y2 - 30y + 63 = 0**

⇒ 3y2 - 30y + 63 = 0

⇒ y2 - 10y + 21 = 0

⇒ y2 - (7 + 3)y + 21 = 0

⇒ y2 - 7y - 3y + 21 = 0

⇒ (y - 7)(y - 3) = 0

⇒ **y = 7, 3**

**Using tabular method for comparison**

Value of x | Value of y | Relation |

5 | 7 | x < y |

5 | 3 | x > y |

3 | 7 | x < y |

3 | 3 | x = y |

**Then we conclude that, **

⇒ **x = y or relation cannot be established**