Question

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

I. x² + x – 210 = 0

II. y² + 3y – 130 = 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 5 : x = y or relationship between x and y cannot be established

Given:

x2 + x – 210 = 0

y2 + 3y – 130 = 0

Calculation:

From I,

x2 + x – 210 = 0

⇒ x² + 15x – 14x – 210 = 0

⇒ x(x + 15) – 14(x + 15) = 0

⇒ (x + 15)(x – 14) = 0

⇒ x = -15, 14

From II,

y2 + 3y – 130 = 0

⇒ y² + 13y – 10y – 130 = 0

⇒ y(y + 13) – 10(y + 13) = 0

⇒ (y + 13)(y – 10) = 0

⇒ y = -13, 10

Comparison between x and y (via Tabulation):

Value of x	Value of y	Relation
-15	-13	x < y
-15	10	x < y
14	-13	x > y
14	10	x > y

∴ The relationship between x and y cannot be established.