Question

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

I. x2 - 20x + 91 = 0

II. y2 + 6y - 91 = 0

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

Answer 1

Correct Answer - Option 3 : x ≥ y

Given:

x2 - 20x + 91 = 0

y2 + 6y - 91 = 0

Calculation:

From I,

x2 - 20x + 91 = 0

⇒ x² - 13x - 7x + 91 = 0

⇒ x(x - 13) - 7(x - 13) = 0

⇒ (x - 7)(x - 13) = 0

⇒ x = 7, 13

From II,

y2 + 6y - 91 = 0

⇒ y² + 13y - 7y - 91 = 0

⇒ y(y + 13) - 7(y + 13) = 0

⇒ (y + 13)(y - 7) = 0

⇒ y = -13, 7

Comparison between x and y (via Tabulation):

Value of x	Value of y	Relation
7	-13	x > y
7	7	x = y
13	-13	x > y
13	7	x > y

 

∴ x ≥ y.