Question

In the following question two equations are given. You have to solve the equations and mark the answer accordingly.

l. x² – 21x + 68 = 0

ll. y² – 31√7y + 1050 = 0

1. x > y
2. x < y
3. x ≥ y
4. x ≤ y
5. x = y or relation between them cannot be established

Answer 1

Correct Answer - Option 5 : x = y or relation between them cannot be established

Calculation:

⇒ x² – 21x + 68 = 0

⇒ x² – 17x – 4x + 68 = 0

⇒ x (x - 17) – 4 (x - 17) = 0

⇒ (x – 4) (x - 17) = 0

⇒ x = 4, 17

⇒ y² – 31√7y + 1050 = 0

⇒ y² – 25√7y – 6√7y + 1050 = 0

⇒ y (y – 25√7) – 6√7(y – 25√7) = 0

⇒ (y – 6√7) (y – 25√7) = 0

⇒ y = 6√7, 25√7

Value of x	Value of y	Relation between x and y
4	6√7 = 15.87	x < y
4	25√7 = 66.14	x < y
17	6√7 = 15.87	x > y
17	25√7 = 66.14	x < y

∴ The relation between x and y cannot be determine.