Question

In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.

I. 5x² – 18x + 9 = 0

II. 3y² + 5y – 2 = 0

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

Answer 1

Correct Answer - Option 1 : x > y

I. 5x2 – 18x + 9 = 0

⇒ 5x² – 15x – 3x + 9 = 0

⇒ 5x (x – 3) –3 (x – 3) = 0

⇒ (5x – 3) (x – 3) = 0

⇒ x = 3/5 or 3

II. 3y2 + 5y – 2 = 0

⇒ 3y² + 6y – y – 2 = 0

⇒ 3y (y + 2) – 1 (y + 2) = 0

⇒ (3y – 1) (y + 2) = 0

⇒ y = 1/3 or –2

Comparison between x and y (via Tabulation):

Value of x	Value of y	Relation
3/5	1/3	x > y
3/5	-2	x > y
3	1/3	x > y
3	-2	x > y

∴ Clearly x > y